Reinforcement Learning for Stock Trading
Rophence Ojiambo & Anusha Kumar
1 Introduction
1.1 Learning by Reward
Imagine you are trying to train a group of monkeys to play basketball. Every time a monkey makes a successful shot, you give it a banana. If the monkey misses the shot, you do not give it a banana. Over time, the monkeys start to associate making successful shots with receiving a banana and start to develop strategies to improve their chances of making a successful shot, such as passing the ball to a teammate or practicing their aim.
Better still, Imagine you are training a robot to do laundry. You set up a reinforcement learning algorithm where the robot receives a positive reward (high five) when it successfully sorts the clothes, adds the correct amount of detergent, and washes the clothes without damaging them. The robot receives a negative reward (no high five) if it damages the clothes, spills detergent, or makes a mistake in the sorting process. At first, the robot has no idea how to do laundry.
It may accidentally mix whites and colors or add too much detergent, resulting in negative rewards. However, through trial and error, the robot gradually learns the correct sequence of actions to take when doing laundry. As the robot continues to do laundry over time, the robot starts to associate successfully washing and drying laundry with receiving a high-five and starts to optimize its laundry skills to maximize the chances of getting a high-five. It refines its strategy and learns to adapt to several types of fabrics and stains. It may adjust the water temperature, or the amount of detergent based on the type of fabric being washed or selecting the correct cycle.
Over time, the robot becomes your skilled laundry assistant, capable of doing laundry efficiently and effectively. Now imagine that you change the scenario by adding a new type of fabric or stain that the robot has never encountered before. The robot may initially struggle to determine the correct cycle or water temperature or detergent amount to use. However, by experimenting with different settings and observing the results, the robot can learn to adjust its strategy to handle the new fabric or stain type. These are just a few examples of reinforcement learning. The robot/monkeys are the agents, the shot/laundry task are the actions, the banana/high-five are the rewards, and the association between the action and the reward is the policy. By using a reward signal to guide the agents’ behavior, you can train them to learn a specific task or behavior. This also demonstrates how reinforcement learning algorithms can adapt to new and unexpected situations, even in complex tasks like doing laundry.
1.2 Stock Trading
How can we teach a 10-year-old to trade stocks? First of all, we start with basics of risks and rewards. Tell them to forget about lemonade stands and allowance money, we are talking real cash here. Let them imagine playing a game where they get to buy and sell imaginary items, like Pokemon cards or Beanie Babies. They should want to buy low and sell high to make a profit, just like in real life. The game is called RL, that's right, it stands for "Real" Life and the stakes are high, but the rewards can be even higher.
Now, here’s where things get tricky. RL isn’t like other games where they can just hit “reset” and start over if you mess up. They have to learn from their mistakes and make smarter choices next time. So, one should do their research, pay attention to trends, and don’t be afraid to take risks (but not too many!). It’s all about balancing risk and reward, just like in RL.
In the world of stock trading, timing is everything. It is no secret that the stock market is unpredictable, with prices rising and falling based on everything from global events to social media trends. Recently, stocks like Bitcoin, Dogecoin, GameStop and Tesla have captured the attention of investors and the public alike[1]. Whether it is buying low and selling high or knowing when to hold onto a stock for the long term, making the right decision can mean the difference between profit and loss. But how can traders stay on top of market trends and make informed decisions in such a volatile environment? Is it possible to automate trading entirely for traders who want to trade 24/7 but do not want to be glued to their screens all the time? One answer is reinforcement learning, a form of machine learning that trains algorithms to learn from past actions and outcomes and make better decisions over time[2,3]. In this project, we will explore the application of reinforcement learning in stock trading and how this can potentially change the way we think about financial investment decisions.
2 What is Reinforcement Learning?
Reinforcement learning (RL) is a type of machine learning algorithm that enables an agent to learn how to make decisions based on rewards and punishments. It involves an agent interacting with an environment, taking actions, receiving feedback, and adjusting its behavior based on that feedback[3]. The goal of RL is to optimize the agent’s behavior to maximize the cumulative reward it receives over time. RL algorithms are used in various applications such as robotics, gaming, finance, and natural language processing[4–7]. RL is based on the concept of trial and error. We can consider an individual placed in an unfamiliar environment. Initially, mistakes may occur, but through learning from them, they can avoid repeating them in the future when faced with similar circumstances. RL employs a similar approach in training its model, whereby the agent tries different actions and observes the resulting rewards or punishments, and then adjusts its behavior to maximize the expected reward in the future.
2.1 Mathematical Nature of Reinforcement Learning
We can illustrate the nature of reinforcement learning as follows: at each sequence of discrete time points (or steps), with t = 0, 1, 2, 3, etc., the agent and environment interact. The agent receives information about the environment’s state, \(s_t\) within S, at each time point/step, t, where S represents the set of possible states, which on this basis, selects an action from A(\(s_t\)), the set of actions to choose from. The agent receives the numerical reward within R, and then finds itself under a new state[8]. The diagram below illustrates this process:
The goal of reinforcement learning (RL) can be summarized as finding a policy that maximizes the expected cumulative reward over a sequence of interactions between an agent and its environment. Mathematically, this can be expressed as:
\[\boldsymbol{maximize~ E[R] = \max_{\pi} E\left[\sum_{t=0}^{\infty} \gamma^t r_t\right]}\]
where \(\boldsymbol{E[R]}\) is the expected cumulative reward, \(\boldsymbol{\gamma}\) is the discount factor (\(0 \leq \gamma \leq 1\)), \(\boldsymbol{r_t}\) is the reward obtained at time \(\boldsymbol{t}\), and the summation is taken over all time steps from \(\boldsymbol{t=0}\) to \(\boldsymbol{t=\infty}\).
The objective function in RL is typically the expected cumulative reward, which is also known as the return. This function is used to evaluate the performance of a policy, which maps states to actions. The objective is to find the policy that maximizes the expected return over a given time horizon.
The objective function can be expressed as:
\[\boldsymbol{J(\pi) = E_{\pi}\left[\sum_{t=0}^{\infty} \gamma^t r_t\right]}\]
where \(\boldsymbol{J(\pi)}\) is the expected return for policy \(\boldsymbol{\pi}\), \(\boldsymbol{E_{\pi}}\) is the expectation over the distribution of trajectories generated by following policy \(\boldsymbol{\pi}\), and the summation is taken over all time steps from \(\boldsymbol{t=0}\) to \(\boldsymbol{t=\infty}\).
The goal of RL is to find the policy \(\boldsymbol{\pi^*}\) that maximizes the objective function \(\boldsymbol{J(\pi)}\), i.e.,
\[\boldsymbol{\pi^* = \arg\max_{\pi} J(\pi)}\] Since the challenge that remains is to nudge the policy parameters such that the return can be maximized, we can meet this goal by using the gradient of the objective function. This is known as vanilla gradient ascent. We should note that gradient descent and gradient ascent are synonymous, with only a sign change being the notable difference (sign change is moved to downhill for gradient descent)[9].
Policy Gradient Theorem
- In step 1, we observe that our goal is to find the gradient of the objective function.
- Then, within step 2, the expected return is replaced with an implementation (can be any of your choice), however it is usually easier to proceed with the action-value function. We denote the expected return as equivalent to each action’s (Q) value multiplied by the probability that the particular action is visited (which is defined by the policy, \(\pi\)).
- We take the gradient with respect to the parameters of the policy. Therefore, we can move Q, the action value function, outside of the calculation of the gradient (as defined in step 3).
- Proceeding with our steps, for step 4, we multiply the entire equation by \(\pi\)(a | s)/\(\pi\)(a | s), which is equivalent to one. Therefore, the equation is not altered.
- For step 5, we proceed with a typical mathematical identity, which replaces the fraction with a natural logarithm. This is a fairly standard computational trick, where we prevent the multiplication of small probabilities, which can make the gradients zero (also known as the vanishing gradient problem).
- Finally, for step 6, we can remember that the summation of action values, which are multiplied by the probabilities for the action, are what we started with in step 2. However, as a substitute to summing over the actions, we instruct the agent to adhere by the policy and return the expectation of the specified action over time[9].
2.2 Key Elements of Reinforcement Learning
Agent: The agent in RL is the decision-making entity that interacts with the environment. In the stock trading analogy, the agent could be the trader who decides when or which stocks to buy and sell.
Environment: The environment in RL is the world in which the agent operates and interacts with. In the stock trading analogy, the environment would be the stock market, which includes all the stocks, their prices, and the various events that affect the market.
State (S): A state in RL refers to the current situation of the environment, as observed by the agent. In the stock trading analogy, a state would include the current prices of the stocks the trader is interested in, the current state of the economy, and any other relevant factors that may influence the decision to buy or sell.
Policy (\(\pi\)): A policy in RL is a set of rules or instructions that the agent uses to determine its actions in a given state. In the stock trading analogy, a policy could be the algorithm that the agent uses to determine which stocks to buy and sell based on the current state.
Action (A): In RL, the action is the decision made by the agent based on the current state and the policy. In the stock trading analogy, the action would be the trader’s decision to hold, buy or sell a specific stock.
Reward (R): A reward in RL is a feedback signal that the agent receives after taking an action. It indicates how good or bad the action was in achieving the agent’s objective. In the stock trading analogy, the reward would be the profit or loss made from the trade.
Penalty: A penalty in RL is a negative feedback signal that the agent receives after taking an action that is not desired or expected. In the stock trading analogy, the penalty would be the loss incurred from a bad trade or missed opportunity..
2.3 Advantages of Reinforcement Learning
Learning through trial and error: Unlike supervised learning, where the algorithm is provided with labeled data, RL algorithms learn by trial and error, without explicit supervision thus making it well-suited for applications where it is difficult or impractical to provide labeled data.
Flexibility: RL can be used in both single-agent and multi-agent settings. In a single-agent setting, the agent learns to optimize its behavior by interacting with the environment while in a multi-agent setting, multiple agents learn to interact with each other and optimize their behavior collectively.
Adaptability: RL algorithms can adapt to changes in the environment and adjust their behavior accordingly. This makes RL well-suited for dynamic and uncertain environments where traditional machine learning approaches may struggle.
Exploration: RL algorithms are designed to explore new strategies and actions in order to maximize their rewards. This can lead to the discovery of novel solutions and approaches that may not have been considered otherwise.
2.4 Challenges of Reinforcement Learning
Exploration-exploitation tradeoff: RL algorithms need to balance between exploring the environment to find new and potentially better actions, and exploiting the knowledge they already have to maximize rewards in the past. This tradeoff can be challenging, especially in complex environments with many possible actions.
Generalization: RL algorithms may struggle to generalize their learned policies to new, unseen environments or tasks that were not encountered during training, which can limit their usefulness in practice. Data efficiency: RL algorithms typically require a large amount of data to learn a good policy, which can be time-consuming and expensive to obtain.
Reward engineering: The quality of the learned policy depends heavily on the reward function used, which can be difficult to design in a way that accurately reflects the desired behavior.
Safety and ethics: RL agents can learn to take actions that are harmful or unethical, especially if the reward function is not carefully designed or the agent’s behavior is not appropriately constrained.
Interpretability: RL algorithms can be difficult to interpret and explain, especially when they use complex models or operate in high-dimensional state and action spaces.
3 Reinforcement Learning Algorithms
There are several categories of reinforcement learning algorithms that can be used for stock trading, including:
Model-Based Reinforcement Learning Algorithms: These algorithms learn the model from data and use it to optimize the agent’s behavior and plan actions that maximize the expected cumulative reward to predict the outcomes of actions. Model-based algorithms are computationally efficient and require less data to learn than model-free algorithms. However, they may suffer from errors in the learned model, which can lead to sub optimal behavior. Examples of model-based reinforcement learning algorithms for stock trading include: Dynamic Programming, Monte Carlo methods and Temporal Difference Learning
Value-Based Reinforcement Learning Algorithms: These are model-free that learn an estimate of the optimal value function and use it to derive an optimal policy. These algorithms are more robust to errors in the environment model, but they require more data to learn and can be computationally expensive. Examples of value-based reinforcement learning algorithms for stock trading include: Q-Learning, Deep Q-Networks (DQNs), and Double DQNs.
Policy-Based Reinforcement Learning Algorithms: These algorithms learn the optimal policy directly, without estimating the value function. Examples of policy-based reinforcement learning algorithms for stock trading include:REINFORCE, SARSA, Proximal Policy Optimization (PPO) and Actor-Critic
Hybrid Reinforcement Learning Algorithms: These algorithms combine elements of value-based and policy-based reinforcement learning. Examples of hybrid reinforcement learning algorithms for stock trading include: Trust Region Policy Optimization (TRPO) and Asynchronous Advantage Actor-Critic (A3C)
In practice, the choice of reinforcement learning algorithm for stock trading depends on the specific task and the characteristics of the environment. For example, a value-based algorithm like DQN may be well-suited for a simple trading environment with discrete actions, while a policy-based algorithm like PPO may be better for a more complex environment with continuous actions.
Each of these algorithms has different advantages and disadvantages, and their performance can vary depending on the specific problem being addressed and on several factors, such as: (1)Efficiency and speed of convergence, (2) Performance on historical data, (3) Robustness to market changes, (4) Ability to handle high-dimensional state and action space, and (5) Interpretability: how easily the algorithm’s decisions can be interpreted and understood. Ultimately, the choice of algorithm will depend on the specific goals of the trader, the particular characteristics of the stock market being traded, and the desired performance metrics.
Next, we expand more on the algorithms we will use for our data
3.1 1. Q-Learning
Q-learning[10] is a popular value-based reinforcement learning algorithm based on the well known Bellman equation:
\[\boldsymbol{V(s) = \mathbb{E}[R_{t+1} + \gamma V(s_{t+1}) | S_t = s]}\] Where; \(\boldsymbol{V(s)}\) is the value of the current state \(s\), \(\mathbb{E}\) refers to the expectation, while \(\gamma\) refers to the discount factor that determines the importance of future rewards. From the above definition of the Bellman’s equation, the action value function can be expressed as:
In Q-learning, the agent uses an iterative approach to update the Q-function estimates and learn an estimate of the optimal action-value based on the rewards obtained from each function. The optimal Q-value, denoted as Q* can be expressed using the law of total probability as:
\[\boldsymbol{Q^*(s, a) = \mathbb{E}{s' \sim p(\cdot|s,a)} \Big[r + \gamma \max_{a'} Q^*(s', a')\Big | s,a\Big]}\] where \(\boldsymbol{s'} \sim \boldsymbol{p(\cdot|s,a)}\) denotes the next state sampled from the transition probability distribution, \(\boldsymbol{p(\cdot|s,a)}\), \(\boldsymbol{r}\) is the immediate reward obtained after taking action \(\boldsymbol{a}\) in state \(\boldsymbol{s}\).
In the context of stock trading, Q-learning can be used to learn the optimal buying and selling decisions for a given stock, based on historical price data and other market indicators. The agent can learn to maximize its expected profit over a given time horizon, taking into account the risks and uncertainties associated with stock trading.
The Q-learning algorithm can be described by the following update rule:
\[\boldsymbol{Q(S_t, A_t) \leftarrow Q(S_t, A_t) + \alpha \Big[R_{t+1} + \gamma \max_a Q(S_{t+1}, a) - Q(S_t, A_t)\Big]}\]
where:
- \(\boldsymbol{Q(S_t, A_t)}\) is the current estimate of the Q-value for state-action pair - \((\boldsymbol{S_t}, \boldsymbol{A_t})\),
- \(\boldsymbol{R_{t+1}}\) is the immediate reward obtained after taking action
- \(\boldsymbol{A_t}\) in the next state \(\boldsymbol{S_{t+1}}\),
- \(\boldsymbol{\alpha}\) is the learning rate,
- \(\boldsymbol{\gamma}\) is the discount factor, and
- \(\boldsymbol{\max_a Q(S_{t+1}, a)}\) is the maximum Q-value over all possible actions in the next state \(\boldsymbol{S_{t+1}}\).
The algorithm is summarized as below:
3.2 2. State-Action-Reward-State-Action (SARSA)
SARSA (State-Action-Reward-State-Action) is a RL algorithm that is used for online and on-policy learning. It is similar to Q-learning, but instead of updating the Q-value of the current state-action pair using the maximum Q-value of the next state, SARSA updates the Q-value using the Q-value of the next state-action pair, that is, it learns the Q-value of the policy being followed[2]. The SARSA algorithm can be described by the following update rule:
\[\boldsymbol{Q(S_t,A_t) \leftarrow Q(S_t,a_t) + \alpha[r_{t+1} + \gamma Q(S_{t+1},a_{t+1}) - Q(S_t,a_t)]}\]
Where:
- \(\boldsymbol{Q(S_t,a_t)}\) is the Q-value of the current state-action pair \((S_t,A_t)\)
- \(\boldsymbol{\alpha}\) is the learning rate that determines the impact of the new information on the existing Q-value
- \(\boldsymbol{r_{t+1}}\) is the immediate reward obtained after taking action \(A_t\) in state \(S_t\)
- \(\boldsymbol{\gamma}\) is the discount factor that determines the importance of future rewards
- \(\boldsymbol{Q(S_{t+1} ,a_{t+1}})\) is the Q-value of the next state-action pair \((S_{t+1},a_{t+1})\) under the current policy. This is the value of the action selected by the agent in the next state.
- \(\boldsymbol{Q(S_t,a_t)}\) is the current estimate of the Q-value of state-action pair \((S_t,a_t)\).
This equation updates the estimate of the Q-value of the current state-action pair by adding the difference between the observed reward and the estimate of the next state-action pair’s Q-value, multiplied by the learning rate \(\alpha\).
The algorithm is summarized as below:
3.2.1 What then is the difference between Q-Learning and SARSA?
From the Q-Learning and SARSA pseudo codes
[obtained from stackoverflow] illustrated in the previous sections, the
blue boxes emphasize the portion where the two algorithms exhibit a
distinction, while the numbers highlight a more intricate difference as
elaborated below.
The key difference between SARSA and Q-learning lies in how the Q-value is updated after each action. In SARSA, the Q-value is updated based on the Q-value of the action chosen using an ε-greedy policy. In contrast, Q-learning selects the maximum Q-value over all possible actions for the next step, which effectively means that no exploration is performed at this stage.
Despite this difference, Q-learning still selects the action based on an ε-greedy policy when taking an actual action. Therefore, the “Choose A …” step is included in the repeat loop.
In Q-learning, the action for the next step is still selected using an ε-greedy policy, following the logic of the loop.
3.3 3. Deep Q-network (DQN)
Deep Q-Network (DQN), is a type of RL algorithm that was introduced in 2015 and uses deep neural networks to approximate the Q-values of state-action pairs in a Markov decision process[11].
The DQN algorithm uses experience replay and target networks to improve the stability and efficiency of the learning process. Experience replay involves storing the agent’s experiences (i.e., state, action, reward, next state) in a replay buffer and sampling mini-batches of experiences randomly from the buffer to train the neural network.
Target networks involve creating a separate neural network with the same architecture as the Q-network but with frozen weights to estimate the target Q-values used in the Bellman equation. This reduces the correlation between the target and predicted Q-values, which improves the stability of the learning process.
The update equation for Deep Q-Network (DQN) algorithm can be written as follows:
\[\boldsymbol{Q(s,a) = Q(s,a) + \alpha [r + \gamma \max_{a'} Q'(s',a') - Q(s,a)]}\]
Where:
- \(\boldsymbol{Q(s,a)}\) is the estimated Q-value for state s and action a;
- \(\boldsymbol{r}\) is the reward obtained after taking action \(a\) in state \(s\);
- \(\boldsymbol{s'}\) is the next state after taking action \(a\) in state $s;
- \(a'\) is the action with the highest Q-value in state \(s'\);
- \(\boldsymbol{Q'(s',a')}\) is the target Q-value for the next state-action pair, computed using a separate target network that is periodically updated with the main network;
- \(\boldsymbol{\alpha}\) is the learning rate;
- \(\boldsymbol{\gamma}\) is the discount factor, which determines the weight given to future rewards.
The algorithm is summarized as below:
3.4 Exploration vs Exploitation
The process of learning in RL is through exploration and exploitation[13].
Exploration involves selecting actions that the agent has not taken before and is a crucial aspect of RL as it helps the agent to enhance its current knowledge of each action by discovering new states and actions that can potentially lead to a higher rewards. By improving the precision of the estimated action-values, the agent can make more informed decisions in the future, leading to better performance.
On the other hand, exploitation selects the action that appears to offer the greatest reward by utilizing the agent’s current action-value estimates. However, pursuing greedy actions based on action-value estimates may not necessarily lead to the optimal solution, resulting in sub-optimal behavior. Exploration provides the agent with more accurate estimates of action-values, whereas exploitation may yield more rewards. However, the agent cannot pursue both simultaneously, creating a dilemma known as the exploration-exploitation tradeoff.
Greedy Policy: The agent takes the action with the maximum Q value at any state in the environment in the greedy policy exploration. This approach ensures the agent takes the optimal action at each step, but it has the obvious shortcoming of never exploring any other action other than the optimal one, leading to sub-optimal solutions.
Epsilon-greedy exploration is another popular exploration strategy in RL, which involves selecting a random action with a certain probability (epsilon) and selecting the action with the highest expected reward with a probability of 1-epsilon[13,14]. Epsilon-greedy exploration strikes a balance between exploration and exploitation, and it is particularly useful when the agent has some prior knowledge of the environment. However, this strategy can lead to sub optimal solutions if the agent gets stuck in a local maximum.
Thompson sampling[15] is a more sophisticated exploration strategy that involves selecting actions based on the probability of their being optimal. This strategy involves maintaining a probability distribution over the possible rewards of each action and then selecting the action with the highest expected reward according to this distribution. Thompson sampling is particularly useful in situations where the environment is complex and dynamic and where it is not clear which actions will lead to a higher reward. However, this strategy can be computationally expensive and difficult to implement in practice.
When implementing the above mentioned algorithms, we mainly apply the
Epsilon-greedy policy.
4 Previous Work
Reinforcement learning (RL) is an effective approach for building intelligent trading agents in stock markets. Among various RL algorithms, Q-learning, SARSA, and Deep Q-Network (DQN) are the most popular ones. Q-learning is a model-free RL algorithm that uses the Q-function to approximate the optimal policy. The Q-value of each action-state pair is updated using the Bellman equation. A recent study conducted by Chakole et. al[16] used the Q-learning algorithm of Reinforcement Learning to train a trading agent for discovering optimal dynamic trading strategies. They conducted experiments using the proposed models on real stock market data from the Indian and American stock markets. The results showed that the proposed models were more profitable compared to the Buy-and-Hold and Decision-Tree based trading strategies.
SARSA is another popular RL algorithm that is used for trading in stock markets. Unlike Q-learning, SARSA is an on-policy algorithm that uses the SARSA Q-function to estimate the expected future rewards. A recent study[17] involved implementing a RL agent with the SARSA algorithm and testing it on 10 stocks from the Brazilian B3 stock market. The experiments indicated that the RL agent was able to generate high profits with lower risks as compared to a supervised learning agent that employed a LSTM neural network.
Deep Q-Network (DQN) is a popular RL algorithm that uses deep neural networks to approximate the Q-function. Another study[18] aimed to create an end-to-end daily stock trading system using Deep Q-network (DQN) and Deep Recurrent Q-network (DRQN) algorithms to automatically decide whether to buy or sell stocks. The S&P500 ETF was used as the trading asset and daily trading data as the state of the trading environment. The performance of the system was compared to benchmarks of Buy and Hold (BH) and Random action-selected DQN trader, and the results showed that the DQN trader outperformed both benchmarks.
When using RL for trading, the figure below shows a general expectation of the trading decisions made by the interaction of the agent and states in the stock trading environment.
5 Application to Stock Data
In this section, we will explore data from the stock market, downloaded from yahoo finance (2010-2022) and show implementation of the RL algorithms discussed in the previous section. Below are the variable descriptions for stock data:
symbol: The name or ticker symbol of the stock, Apple (AAPL), Amazon (AMZN), Johnson & Johnson stock (JNJ), and NFLX.
date: The date of the stock price.
open: The opening price of the stock on a given day.
high: The highest price that the stock traded at during the day.
low: The lowest price that the stock traded at during the day.
close The price at which the stock closed for trading on that particular day.
volume:The number of shares of the stock that were traded on a given day.
adjusted: The adjusted closing price of the stock on a given day, which takes into account any corporate actions, such as stock splits or dividends, that affect the stock price.
To download stock data for Apple, Amazon, Johnson & Johnson, and
Netflix in R, we can use the tidyquant package.
library(tidyquant) # for stock data
# Define a vector with the stock symbols of interest
symbols <- c("AAPL", "AMZN", "JNJ", "NFLX")
# Use the tq_get() function to download the stock data for each symbol and bind them into one data frame
stocks_data <- symbols %>%
tq_get(get = "stock.prices", from = "2010-01-01", to = "2022-12-31") %>%
group_by(symbol) %>%
mutate(date = as.Date(date)) %>%
ungroup() %>%
select(symbol, date, everything())5.1 Implementation of Q-learning
Our code implements the Q-learning algorithm to create a simple trading strategy for stocks. The Q-learning algorithm is a model-free reinforcement learning technique used to learn an optimal policy based on trial and error. It involves building a Q-table that maps the current state and action to the expected future reward. In this case, the state is the current stock price, and the action is either to buy or hold/sell.
The function ‘Q_learning’ takes a data frame of stock prices and applies the Q-learning algorithm to each stock to create a Q-matrix that stores the expected future rewards for each state-action pair. It also creates a list of Boolean Q-tables for each stock, which specify whether to buy or hold/sell at each time step based on the Q-matrix. Finally, it returns the Q-matrix, actions taken, and Q-table for each stock.
Our code then loads stock data for four companies “AAPL”, “AMZN”, “JNJ”, “NFLX”, extracts the adjusted prices, and combines them into a matrix. It performs exploratory data analysis (EDA) by plotting the distribution of prices for each stock. It then applies the ‘Q_learning’ function to each stock to create a list of Q-matrices, actions taken, and Q-tables.
The ‘Q_learning_summary’ function generates a summary table of the actions taken for each stock, converts the action codes to action names, and splits the summary table by stock. It then creates tables for action for each stock and access the Q matrix for each stock. The ‘predict_prices’ function predicts the prices of a stock using the Q matrix and the current prices of the stock.
## Stock Action_Taken
## 1 AAPL Sell
## 2 AAPL Sell
## 3 AAPL Sell
## 4 AAPL Sell
## 5 AAPL Buy
## 6 AAPL Buy
## 7 AAPL Buy
## 8 AAPL Buy
## 9 AAPL Buy
## 10 AAPL Buy
## 11 AAPL Buy
## 12 AAPL Buy
## 13 AAPL Buy
## 14 AAPL Buy
## 15 AAPL Buy
## 16 AAPL Buy
## 17 AAPL Buy
## 18 AAPL Buy
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## 25 AAPL Buy
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## 2921 AAPL Buy
## 2922 AAPL Buy
## 2923 AAPL Buy
## 2924 AAPL Buy
## 2925 AAPL Buy
## 2926 AAPL Buy
## 2927 AAPL Buy
## 2928 AAPL Buy
## 2929 AAPL Buy
## 2930 AAPL Buy
## 2931 AAPL Buy
## 2932 AAPL Buy
## 2933 AAPL Buy
## 2934 AAPL Buy
## 2935 AAPL Buy
## 2936 AAPL Buy
## 2937 AAPL Buy
## 2938 AAPL Buy
## 2939 AAPL Buy
## 2940 AAPL Buy
## 2941 AAPL Buy
## 2942 AAPL Buy
## 2943 AAPL Buy
## 2944 AAPL Buy
## 2945 AAPL Buy
## 2946 AAPL Buy
## 2947 AAPL Buy
## 2948 AAPL Buy
## 2949 AAPL Buy
## 2950 AAPL Buy
## 2951 AAPL Buy
## 2952 AAPL Buy
## 2953 AAPL Buy
## 2954 AAPL Buy
## 2955 AAPL Buy
## 2956 AAPL Buy
## 2957 AAPL Buy
## 2958 AAPL Buy
## 2959 AAPL Buy
## 2960 AAPL Buy
## 2961 AAPL Buy
## 2962 AAPL Buy
## 2963 AAPL Buy
## 2964 AAPL Buy
## 2965 AAPL Buy
## 2966 AAPL Buy
## 2967 AAPL Buy
## 2968 AAPL Buy
## 2969 AAPL Buy
## 2970 AAPL Buy
## 2971 AAPL Buy
## 2972 AAPL Buy
## 2973 AAPL Buy
## 2974 AAPL Buy
## 2975 AAPL Buy
## 2976 AAPL Buy
## 2977 AAPL Buy
## 2978 AAPL Buy
## 2979 AAPL Buy
## 2980 AAPL Buy
## 2981 AAPL Buy
## 2982 AAPL Buy
## 2983 AAPL Buy
## 2984 AAPL Buy
## 2985 AAPL Buy
## 2986 AAPL Buy
## 2987 AAPL Buy
## 2988 AAPL Buy
## 2989 AAPL Buy
## 2990 AAPL Buy
## 2991 AAPL Buy
## 2992 AAPL Buy
## 2993 AAPL Buy
## 2994 AAPL Buy
## 2995 AAPL Buy
## 2996 AAPL Buy
## 2997 AAPL Buy
## 2998 AAPL Buy
## 2999 AAPL Buy
## 3000 AAPL Buy
## 3001 AAPL Buy
## 3002 AAPL Buy
## 3003 AAPL Buy
## 3004 AAPL Buy
## 3005 AAPL Buy
## 3006 AAPL Buy
## 3007 AAPL Buy
## 3008 AAPL Buy
## 3009 AAPL Buy
## 3010 AAPL Buy
## 3011 AAPL Buy
## 3012 AAPL Buy
## 3013 AAPL Buy
## 3014 AAPL Buy
## 3015 AAPL Buy
## 3016 AAPL Buy
## 3017 AAPL Buy
## 3018 AAPL Buy
## 3019 AAPL Buy
## 3020 AAPL Buy
## 3021 AAPL Buy
## 3022 AAPL Buy
## 3023 AAPL Buy
## 3024 AAPL Buy
## 3025 AAPL Buy
## 3026 AAPL Buy
## 3027 AAPL Buy
## 3028 AAPL Buy
## 3029 AAPL Buy
## 3030 AAPL Buy
## 3031 AAPL Buy
## 3032 AAPL Buy
## 3033 AAPL Buy
## 3034 AAPL Buy
## 3035 AAPL Buy
## 3036 AAPL Buy
## 3037 AAPL Buy
## 3038 AAPL Buy
## 3039 AAPL Buy
## 3040 AAPL Buy
## 3041 AAPL Buy
## 3042 AAPL Buy
## 3043 AAPL Buy
## 3044 AAPL Buy
## 3045 AAPL Buy
## 3046 AAPL Buy
## 3047 AAPL Buy
## 3048 AAPL Buy
## 3049 AAPL Buy
## 3050 AAPL Buy
## 3051 AAPL Buy
## 3052 AAPL Buy
## 3053 AAPL Buy
## 3054 AAPL Buy
## 3055 AAPL Buy
## 3056 AAPL Buy
## 3057 AAPL Buy
## 3058 AAPL Buy
## 3059 AAPL Buy
## 3060 AAPL Buy
## 3061 AAPL Buy
## 3062 AAPL Buy
## 3063 AAPL Buy
## 3064 AAPL Buy
## 3065 AAPL Buy
## 3066 AAPL Buy
## 3067 AAPL Buy
## 3068 AAPL Buy
## 3069 AAPL Buy
## 3070 AAPL Buy
## 3071 AAPL Buy
## 3072 AAPL Buy
## 3073 AAPL Buy
## 3074 AAPL Buy
## 3075 AAPL Buy
## 3076 AAPL Buy
## 3077 AAPL Buy
## 3078 AAPL Buy
## 3079 AAPL Buy
## 3080 AAPL Buy
## 3081 AAPL Buy
## 3082 AAPL Buy
## 3083 AAPL Buy
## 3084 AAPL Buy
## 3085 AAPL Buy
## 3086 AAPL Buy
## 3087 AAPL Buy
## 3088 AAPL Buy
## 3089 AAPL Buy
## 3090 AAPL Buy
## 3091 AAPL Buy
## 3092 AAPL Buy
## 3093 AAPL Buy
## 3094 AAPL Buy
## 3095 AAPL Buy
## 3096 AAPL Buy
## 3097 AAPL Buy
## 3098 AAPL Buy
## 3099 AAPL Buy
## 3100 AAPL Buy
## 3101 AAPL Buy
## 3102 AAPL Buy
## 3103 AAPL Buy
## 3104 AAPL Buy
## 3105 AAPL Buy
## 3106 AAPL Buy
## 3107 AAPL Buy
## 3108 AAPL Buy
## 3109 AAPL Buy
## 3110 AAPL Buy
## 3111 AAPL Buy
## 3112 AAPL Buy
## 3113 AAPL Buy
## 3114 AAPL Buy
## 3115 AAPL Buy
## 3116 AAPL Buy
## 3117 AAPL Buy
## 3118 AAPL Buy
## 3119 AAPL Buy
## 3120 AAPL Buy
## 3121 AAPL Buy
## 3122 AAPL Buy
## 3123 AAPL Buy
## 3124 AAPL Buy
## 3125 AAPL Buy
## 3126 AAPL Buy
## 3127 AAPL Buy
## 3128 AAPL Buy
## 3129 AAPL Buy
## 3130 AAPL Buy
## 3131 AAPL Buy
## 3132 AAPL Buy
## 3133 AAPL Buy
## 3134 AAPL Buy
## 3135 AAPL Buy
## 3136 AAPL Buy
## 3137 AAPL Buy
## 3138 AAPL Buy
## 3139 AAPL Buy
## 3140 AAPL Buy
## 3141 AAPL Buy
## 3142 AAPL Buy
## 3143 AAPL Buy
## 3144 AAPL Buy
## 3145 AAPL Buy
## 3146 AAPL Buy
## 3147 AAPL Buy
## 3148 AAPL Buy
## 3149 AAPL Buy
## 3150 AAPL Buy
## 3151 AAPL Buy
## 3152 AAPL Buy
## 3153 AAPL Buy
## 3154 AAPL Buy
## 3155 AAPL Buy
## 3156 AAPL Buy
## 3157 AAPL Buy
## 3158 AAPL Buy
## 3159 AAPL Buy
## 3160 AAPL Buy
## 3161 AAPL Buy
## 3162 AAPL Buy
## 3163 AAPL Buy
## 3164 AAPL Buy
## 3165 AAPL Buy
## 3166 AAPL Buy
## 3167 AAPL Buy
## 3168 AAPL Buy
## 3169 AAPL Buy
## 3170 AAPL Buy
## 3171 AAPL Buy
## 3172 AAPL Buy
## 3173 AAPL Buy
## 3174 AAPL Buy
## 3175 AAPL Buy
## 3176 AAPL Buy
## 3177 AAPL Buy
## 3178 AAPL Buy
## 3179 AAPL Buy
## 3180 AAPL Buy
## 3181 AAPL Buy
## 3182 AAPL Buy
## 3183 AAPL Buy
## 3184 AAPL Buy
## 3185 AAPL Buy
## 3186 AAPL Buy
## 3187 AAPL Buy
## 3188 AAPL Buy
## 3189 AAPL Buy
## 3190 AAPL Buy
## 3191 AAPL Buy
## 3192 AAPL Buy
## 3193 AAPL Buy
## 3194 AAPL Buy
## 3195 AAPL Buy
## 3196 AAPL Buy
## 3197 AAPL Buy
## 3198 AAPL Buy
## 3199 AAPL Buy
## 3200 AAPL Buy
## 3201 AAPL Buy
## 3202 AAPL Buy
## 3203 AAPL Buy
## 3204 AAPL Buy
## 3205 AAPL Buy
## 3206 AAPL Buy
## 3207 AAPL Buy
## 3208 AAPL Buy
## 3209 AAPL Buy
## 3210 AAPL Buy
## 3211 AAPL Buy
## 3212 AAPL Buy
## 3213 AAPL Buy
## 3214 AAPL Buy
## 3215 AAPL Buy
## 3216 AAPL Buy
## 3217 AAPL Buy
## 3218 AAPL Buy
## 3219 AAPL Buy
## 3220 AAPL Buy
## 3221 AAPL Buy
## 3222 AAPL Buy
## 3223 AAPL Buy
## 3224 AAPL Buy
## 3225 AAPL Buy
## 3226 AAPL Buy
## 3227 AAPL Buy
## 3228 AAPL Buy
## 3229 AAPL Buy
## 3230 AAPL Buy
## 3231 AAPL Buy
## 3232 AAPL Buy
## 3233 AAPL Buy
## 3234 AAPL Buy
## 3235 AAPL Buy
## 3236 AAPL Buy
## 3237 AAPL Buy
## 3238 AAPL Buy
## 3239 AAPL Buy
## 3240 AAPL Buy
## 3241 AAPL Buy
## 3242 AAPL Buy
## 3243 AAPL Buy
## 3244 AAPL Buy
## 3245 AAPL Buy
## 3246 AAPL Buy
## 3247 AAPL Buy
## 3248 AAPL Buy
## 3249 AAPL Buy
## 3250 AAPL Buy
## 3251 AAPL Buy
## 3252 AAPL Buy
## 3253 AAPL Buy
## 3254 AAPL Buy
## 3255 AAPL Buy
## 3256 AAPL Buy
## 3257 AAPL Buy
## 3258 AAPL Buy
## 3259 AAPL Buy
## 3260 AAPL Buy
## 3261 AAPL Buy
## 3262 AAPL Buy
## 3263 AAPL Buy
## 3264 AAPL Buy
## 3265 AAPL Buy
## 3266 AAPL Buy
## 3267 AAPL Buy
## 3268 AAPL Buy
## 3269 AAPL Buy
## 3270 AAPL Buy
## 3271 AAPL Buy
## 3272 AMZN Sell
## 3273 AMZN Sell
## 3274 AMZN Sell
## 3275 AMZN Sell
## 3276 AMZN Buy
## 3277 AMZN Buy
## 3278 AMZN Buy
## 3279 AMZN Buy
## 3280 AMZN Buy
## 3281 AMZN Buy
## 3282 AMZN Buy
## 3283 AMZN Buy
## 3284 AMZN Buy
## 3285 AMZN Buy
## 3286 AMZN Buy
## 3287 AMZN Buy
## 3288 AMZN Buy
## 3289 AMZN Buy
## 3290 AMZN Buy
## 3291 AMZN Buy
## 3292 AMZN Buy
## 3293 AMZN Buy
## 3294 AMZN Buy
## 3295 AMZN Buy
## 3296 AMZN Buy
## 3297 AMZN Buy
## 3298 AMZN Buy
## 3299 AMZN Buy
## 3300 AMZN Buy
## 3301 AMZN Buy
## 3302 AMZN Buy
## 3303 AMZN Buy
## 3304 AMZN Buy
## 3305 AMZN Buy
## 3306 AMZN Buy
## 3307 AMZN Buy
## 3308 AMZN Buy
## 3309 AMZN Buy
## 3310 AMZN Buy
## 3311 AMZN Buy
## 3312 AMZN Buy
## 3313 AMZN Buy
## 3314 AMZN Buy
## 3315 AMZN Buy
## 3316 AMZN Buy
## 3317 AMZN Buy
## 3318 AMZN Buy
## 3319 AMZN Buy
## 3320 AMZN Buy
## 3321 AMZN Buy
## 3322 AMZN Buy
## 3323 AMZN Buy
## 3324 AMZN Buy
## 3325 AMZN Buy
## 3326 AMZN Buy
## 3327 AMZN Buy
## 3328 AMZN Buy
## 3329 AMZN Buy
## 3330 AMZN Buy
## 3331 AMZN Buy
## 3332 AMZN Buy
## 3333 AMZN Buy
## 3334 AMZN Buy
## 3335 AMZN Buy
## 3336 AMZN Buy
## 3337 AMZN Buy
## 3338 AMZN Buy
## 3339 AMZN Buy
## 3340 AMZN Buy
## 3341 AMZN Buy
## 3342 AMZN Buy
## 3343 AMZN Buy
## 3344 AMZN Buy
## 3345 AMZN Buy
## 3346 AMZN Buy
## 3347 AMZN Buy
## 3348 AMZN Buy
## 3349 AMZN Buy
## 3350 AMZN Buy
## 3351 AMZN Buy
## 3352 AMZN Buy
## 3353 AMZN Buy
## 3354 AMZN Buy
## 3355 AMZN Buy
## 3356 AMZN Buy
## 3357 AMZN Buy
## 3358 AMZN Buy
## 3359 AMZN Buy
## 3360 AMZN Buy
## 3361 AMZN Buy
## 3362 AMZN Buy
## 3363 AMZN Buy
## 3364 AMZN Buy
## 3365 AMZN Buy
## 3366 AMZN Buy
## 3367 AMZN Buy
## 3368 AMZN Buy
## 3369 AMZN Buy
## 3370 AMZN Buy
## 3371 AMZN Buy
## 3372 AMZN Buy
## 3373 AMZN Buy
## 3374 AMZN Buy
## 3375 AMZN Buy
## 3376 AMZN Buy
## 3377 AMZN Buy
## 3378 AMZN Buy
## 3379 AMZN Buy
## 3380 AMZN Buy
## 3381 AMZN Buy
## 3382 AMZN Buy
## 3383 AMZN Buy
## 3384 AMZN Buy
## 3385 AMZN Buy
## 3386 AMZN Buy
## 3387 AMZN Buy
## 3388 AMZN Buy
## 3389 AMZN Buy
## 3390 AMZN Buy
## 3391 AMZN Buy
## 3392 AMZN Buy
## 3393 AMZN Buy
## 3394 AMZN Buy
## 3395 AMZN Buy
## 3396 AMZN Buy
## 3397 AMZN Buy
## 3398 AMZN Buy
## 3399 AMZN Buy
## 3400 AMZN Buy
## 3401 AMZN Buy
## 3402 AMZN Buy
## 3403 AMZN Buy
## 3404 AMZN Buy
## 3405 AMZN Buy
## 3406 AMZN Buy
## 3407 AMZN Buy
## 3408 AMZN Buy
## 3409 AMZN Buy
## 3410 AMZN Buy
## 3411 AMZN Buy
## 3412 AMZN Buy
## 3413 AMZN Buy
## 3414 AMZN Buy
## 3415 AMZN Buy
## 3416 AMZN Buy
## 3417 AMZN Buy
## 3418 AMZN Buy
## 3419 AMZN Buy
## 3420 AMZN Buy
## 3421 AMZN Buy
## 3422 AMZN Buy
## 3423 AMZN Buy
## 3424 AMZN Buy
## 3425 AMZN Buy
## 3426 AMZN Buy
## 3427 AMZN Buy
## 3428 AMZN Buy
## 3429 AMZN Buy
## 3430 AMZN Buy
## 3431 AMZN Buy
## 3432 AMZN Buy
## 3433 AMZN Buy
## 3434 AMZN Buy
## 3435 AMZN Buy
## 3436 AMZN Buy
## 3437 AMZN Buy
## 3438 AMZN Buy
## 3439 AMZN Buy
## 3440 AMZN Buy
## 3441 AMZN Buy
## 3442 AMZN Buy
## 3443 AMZN Buy
## 3444 AMZN Buy
## 3445 AMZN Buy
## 3446 AMZN Buy
## 3447 AMZN Buy
## 3448 AMZN Buy
## 3449 AMZN Buy
## 3450 AMZN Buy
## 3451 AMZN Buy
## 3452 AMZN Buy
## 3453 AMZN Buy
## 3454 AMZN Buy
## 3455 AMZN Buy
## 3456 AMZN Buy
## 3457 AMZN Buy
## 3458 AMZN Buy
## 3459 AMZN Buy
## 3460 AMZN Buy
## 3461 AMZN Buy
## 3462 AMZN Buy
## 3463 AMZN Buy
## 3464 AMZN Buy
## 3465 AMZN Buy
## 3466 AMZN Buy
## 3467 AMZN Buy
## 3468 AMZN Buy
## 3469 AMZN Buy
## 3470 AMZN Buy
## 3471 AMZN Buy
## 3472 AMZN Buy
## 3473 AMZN Buy
## 3474 AMZN Buy
## 3475 AMZN Buy
## 3476 AMZN Buy
## 3477 AMZN Buy
## 3478 AMZN Buy
## 3479 AMZN Buy
## 3480 AMZN Buy
## 3481 AMZN Buy
## 3482 AMZN Buy
## 3483 AMZN Buy
## 3484 AMZN Buy
## 3485 AMZN Buy
## 3486 AMZN Buy
## 3487 AMZN Buy
## 3488 AMZN Buy
## 3489 AMZN Buy
## 3490 AMZN Buy
## 3491 AMZN Buy
## 3492 AMZN Buy
## 3493 AMZN Buy
## 3494 AMZN Buy
## 3495 AMZN Buy
## 3496 AMZN Buy
## 3497 AMZN Buy
## 3498 AMZN Buy
## 3499 AMZN Buy
## 3500 AMZN Buy
## 3501 AMZN Buy
## 3502 AMZN Buy
## 3503 AMZN Buy
## 3504 AMZN Buy
## 3505 AMZN Buy
## 3506 AMZN Buy
## 3507 AMZN Buy
## 3508 AMZN Buy
## 3509 AMZN Buy
## 3510 AMZN Buy
## 3511 AMZN Buy
## 3512 AMZN Buy
## 3513 AMZN Buy
## 3514 AMZN Buy
## 3515 AMZN Buy
## 3516 AMZN Buy
## 3517 AMZN Buy
## 3518 AMZN Buy
## 3519 AMZN Buy
## 3520 AMZN Buy
## 3521 AMZN Buy
## 3522 AMZN Buy
## 3523 AMZN Buy
## 3524 AMZN Buy
## 3525 AMZN Buy
## 3526 AMZN Buy
## 3527 AMZN Buy
## 3528 AMZN Buy
## 3529 AMZN Buy
## 3530 AMZN Buy
## 3531 AMZN Buy
## 3532 AMZN Buy
## 3533 AMZN Buy
## 3534 AMZN Buy
## 3535 AMZN Buy
## 3536 AMZN Buy
## 3537 AMZN Buy
## 3538 AMZN Buy
## 3539 AMZN Buy
## 3540 AMZN Buy
## 3541 AMZN Buy
## 3542 AMZN Buy
## 3543 AMZN Buy
## 3544 AMZN Buy
## 3545 AMZN Buy
## 3546 AMZN Buy
## 3547 AMZN Buy
## 3548 AMZN Buy
## 3549 AMZN Buy
## 3550 AMZN Buy
## 3551 AMZN Buy
## 3552 AMZN Buy
## 3553 AMZN Buy
## 3554 AMZN Buy
## 3555 AMZN Buy
## 3556 AMZN Buy
## 3557 AMZN Buy
## 3558 AMZN Buy
## 3559 AMZN Buy
## 3560 AMZN Buy
## 3561 AMZN Buy
## 3562 AMZN Buy
## 3563 AMZN Buy
## 3564 AMZN Buy
## 3565 AMZN Buy
## 3566 AMZN Buy
## 3567 AMZN Buy
## 3568 AMZN Buy
## 3569 AMZN Buy
## 3570 AMZN Buy
## 3571 AMZN Buy
## 3572 AMZN Buy
## 3573 AMZN Buy
## 3574 AMZN Buy
## 3575 AMZN Buy
## 3576 AMZN Buy
## 3577 AMZN Buy
## 3578 AMZN Buy
## 3579 AMZN Buy
## 3580 AMZN Buy
## 3581 AMZN Buy
## 3582 AMZN Buy
## 3583 AMZN Buy
## 3584 AMZN Buy
## 3585 AMZN Buy
## 3586 AMZN Buy
## 3587 AMZN Buy
## 3588 AMZN Buy
## 3589 AMZN Buy
## 3590 AMZN Buy
## 3591 AMZN Buy
## 3592 AMZN Buy
## 3593 AMZN Buy
## 3594 AMZN Buy
## 3595 AMZN Buy
## 3596 AMZN Buy
## 3597 AMZN Buy
## 3598 AMZN Buy
## 3599 AMZN Buy
## 3600 AMZN Buy
## 3601 AMZN Buy
## 3602 AMZN Buy
## 3603 AMZN Buy
## 3604 AMZN Buy
## 3605 AMZN Buy
## 3606 AMZN Buy
## 3607 AMZN Buy
## 3608 AMZN Buy
## 3609 AMZN Buy
## 3610 AMZN Buy
## 3611 AMZN Buy
## 3612 AMZN Buy
## 3613 AMZN Buy
## 3614 AMZN Buy
## 3615 AMZN Buy
## 3616 AMZN Buy
## 3617 AMZN Buy
## 3618 AMZN Buy
## 3619 AMZN Buy
## 3620 AMZN Buy
## 3621 AMZN Buy
## 3622 AMZN Buy
## 3623 AMZN Buy
## 3624 AMZN Buy
## 3625 AMZN Buy
## 3626 AMZN Buy
## 3627 AMZN Buy
## 3628 AMZN Buy
## 3629 AMZN Buy
## 3630 AMZN Buy
## 3631 AMZN Buy
## 3632 AMZN Buy
## 3633 AMZN Buy
## 3634 AMZN Buy
## 3635 AMZN Buy
## 3636 AMZN Buy
## 3637 AMZN Buy
## 3638 AMZN Buy
## 3639 AMZN Buy
## 3640 AMZN Buy
## 3641 AMZN Buy
## 3642 AMZN Buy
## 3643 AMZN Buy
## 3644 AMZN Buy
## 3645 AMZN Buy
## 3646 AMZN Buy
## 3647 AMZN Buy
## 3648 AMZN Buy
## 3649 AMZN Buy
## 3650 AMZN Buy
## 3651 AMZN Buy
## 3652 AMZN Buy
## 3653 AMZN Buy
## 3654 AMZN Buy
## 3655 AMZN Buy
## 3656 AMZN Buy
## 3657 AMZN Buy
## 3658 AMZN Buy
## 3659 AMZN Buy
## 3660 AMZN Buy
## 3661 AMZN Buy
## 3662 AMZN Buy
## 3663 AMZN Buy
## 3664 AMZN Buy
## 3665 AMZN Buy
## 3666 AMZN Buy
## 3667 AMZN Buy
## 3668 AMZN Buy
## 3669 AMZN Buy
## 3670 AMZN Buy
## 3671 AMZN Buy
## 3672 AMZN Buy
## 3673 AMZN Buy
## 3674 AMZN Buy
## 3675 AMZN Buy
## 3676 AMZN Buy
## 3677 AMZN Buy
## 3678 AMZN Buy
## 3679 AMZN Buy
## 3680 AMZN Buy
## 3681 AMZN Buy
## 3682 AMZN Buy
## 3683 AMZN Buy
## 3684 AMZN Buy
## 3685 AMZN Buy
## 3686 AMZN Buy
## 3687 AMZN Buy
## 3688 AMZN Buy
## 3689 AMZN Buy
## 3690 AMZN Buy
## 3691 AMZN Buy
## 3692 AMZN Buy
## 3693 AMZN Buy
## 3694 AMZN Buy
## 3695 AMZN Buy
## 3696 AMZN Buy
## 3697 AMZN Buy
## 3698 AMZN Buy
## 3699 AMZN Buy
## 3700 AMZN Buy
## 3701 AMZN Buy
## 3702 AMZN Buy
## 3703 AMZN Buy
## 3704 AMZN Buy
## 3705 AMZN Buy
## 3706 AMZN Buy
## 3707 AMZN Buy
## 3708 AMZN Buy
## 3709 AMZN Buy
## 3710 AMZN Buy
## 3711 AMZN Buy
## 3712 AMZN Buy
## 3713 AMZN Buy
## 3714 AMZN Buy
## 3715 AMZN Buy
## 3716 AMZN Buy
## 3717 AMZN Buy
## 3718 AMZN Buy
## 3719 AMZN Buy
## 3720 AMZN Buy
## 3721 AMZN Buy
## 3722 AMZN Buy
## 3723 AMZN Buy
## 3724 AMZN Buy
## 3725 AMZN Buy
## 3726 AMZN Buy
## 3727 AMZN Buy
## 3728 AMZN Buy
## 3729 AMZN Buy
## 3730 AMZN Buy
## 3731 AMZN Buy
## 3732 AMZN Buy
## 3733 AMZN Buy
## 3734 AMZN Buy
## 3735 AMZN Buy
## 3736 AMZN Buy
## 3737 AMZN Buy
## 3738 AMZN Buy
## 3739 AMZN Buy
## 3740 AMZN Buy
## 3741 AMZN Buy
## 3742 AMZN Buy
## 3743 AMZN Buy
## 3744 AMZN Buy
## 3745 AMZN Buy
## 3746 AMZN Buy
## 3747 AMZN Buy
## 3748 AMZN Buy
## 3749 AMZN Buy
## 3750 AMZN Buy
## 3751 AMZN Buy
## 3752 AMZN Buy
## 3753 AMZN Buy
## 3754 AMZN Buy
## 3755 AMZN Buy
## 3756 AMZN Buy
## 3757 AMZN Buy
## 3758 AMZN Buy
## 3759 AMZN Buy
## 3760 AMZN Buy
## 3761 AMZN Buy
## 3762 AMZN Buy
## 3763 AMZN Buy
## 3764 AMZN Buy
## 3765 AMZN Buy
## 3766 AMZN Buy
## 3767 AMZN Buy
## 3768 AMZN Buy
## 3769 AMZN Buy
## 3770 AMZN Buy
## 3771 AMZN Buy
## 3772 AMZN Buy
## 3773 AMZN Buy
## 3774 AMZN Buy
## 3775 AMZN Buy
## 3776 AMZN Buy
## 3777 AMZN Buy
## 3778 AMZN Buy
## 3779 AMZN Buy
## 3780 AMZN Buy
## 3781 AMZN Buy
## 3782 AMZN Buy
## 3783 AMZN Buy
## 3784 AMZN Buy
## 3785 AMZN Buy
## 3786 AMZN Buy
## 3787 AMZN Buy
## 3788 AMZN Buy
## 3789 AMZN Buy
## 3790 AMZN Buy
## 3791 AMZN Buy
## 3792 AMZN Buy
## 3793 AMZN Buy
## 3794 AMZN Buy
## 3795 AMZN Buy
## 3796 AMZN Buy
## 3797 AMZN Buy
## 3798 AMZN Buy
## 3799 AMZN Buy
## 3800 AMZN Buy
## 3801 AMZN Buy
## 3802 AMZN Buy
## 3803 AMZN Buy
## 3804 AMZN Buy
## 3805 AMZN Buy
## 3806 AMZN Buy
## 3807 AMZN Buy
## 3808 AMZN Buy
## 3809 AMZN Buy
## 3810 AMZN Buy
## 3811 AMZN Buy
## 3812 AMZN Buy
## 3813 AMZN Buy
## 3814 AMZN Buy
## 3815 AMZN Buy
## 3816 AMZN Buy
## 3817 AMZN Buy
## 3818 AMZN Buy
## 3819 AMZN Buy
## 3820 AMZN Buy
## 3821 AMZN Buy
## 3822 AMZN Buy
## 3823 AMZN Buy
## 3824 AMZN Buy
## 3825 AMZN Buy
## 3826 AMZN Buy
## 3827 AMZN Buy
## 3828 AMZN Buy
## 3829 AMZN Buy
## 3830 AMZN Buy
## 3831 AMZN Buy
## 3832 AMZN Buy
## 3833 AMZN Buy
## 3834 AMZN Buy
## 3835 AMZN Buy
## 3836 AMZN Buy
## 3837 AMZN Buy
## 3838 AMZN Buy
## 3839 AMZN Buy
## 3840 AMZN Buy
## 3841 AMZN Buy
## 3842 AMZN Buy
## 3843 AMZN Buy
## 3844 AMZN Buy
## 3845 AMZN Buy
## 3846 AMZN Buy
## 3847 AMZN Buy
## 3848 AMZN Buy
## 3849 AMZN Buy
## 3850 AMZN Buy
## 3851 AMZN Buy
## 3852 AMZN Buy
## 3853 AMZN Buy
## 3854 AMZN Buy
## 3855 AMZN Buy
## 3856 AMZN Buy
## 3857 AMZN Buy
## 3858 AMZN Buy
## 3859 AMZN Buy
## 3860 AMZN Buy
## 3861 AMZN Buy
## 3862 AMZN Buy
## 3863 AMZN Buy
## 3864 AMZN Buy
## 3865 AMZN Buy
## 3866 AMZN Buy
## 3867 AMZN Buy
## 3868 AMZN Buy
## 3869 AMZN Buy
## 3870 AMZN Buy
## 3871 AMZN Buy
## 3872 AMZN Buy
## 3873 AMZN Buy
## 3874 AMZN Buy
## 3875 AMZN Buy
## 3876 AMZN Buy
## 3877 AMZN Buy
## 3878 AMZN Buy
## 3879 AMZN Buy
## 3880 AMZN Buy
## 3881 AMZN Buy
## 3882 AMZN Buy
## 3883 AMZN Buy
## 3884 AMZN Buy
## 3885 AMZN Buy
## 3886 AMZN Buy
## 3887 AMZN Buy
## 3888 AMZN Buy
## 3889 AMZN Buy
## 3890 AMZN Buy
## 3891 AMZN Buy
## 3892 AMZN Buy
## 3893 AMZN Buy
## 3894 AMZN Buy
## 3895 AMZN Buy
## 3896 AMZN Buy
## 3897 AMZN Buy
## 3898 AMZN Buy
## 3899 AMZN Buy
## 3900 AMZN Buy
## 3901 AMZN Buy
## 3902 AMZN Buy
## 3903 AMZN Buy
## 3904 AMZN Buy
## 3905 AMZN Buy
## 3906 AMZN Buy
## 3907 AMZN Buy
## 3908 AMZN Buy
## 3909 AMZN Buy
## 3910 AMZN Buy
## 3911 AMZN Buy
## 3912 AMZN Buy
## 3913 AMZN Buy
## 3914 AMZN Buy
## 3915 AMZN Buy
## 3916 AMZN Buy
## 3917 AMZN Buy
## 3918 AMZN Buy
## 3919 AMZN Buy
## 3920 AMZN Buy
## 3921 AMZN Buy
## 3922 AMZN Buy
## 3923 AMZN Buy
## 3924 AMZN Buy
## 3925 AMZN Buy
## 3926 AMZN Buy
## 3927 AMZN Buy
## 3928 AMZN Buy
## 3929 AMZN Buy
## 3930 AMZN Buy
## 3931 AMZN Buy
## 3932 AMZN Buy
## 3933 AMZN Buy
## 3934 AMZN Buy
## 3935 AMZN Buy
## 3936 AMZN Buy
## 3937 AMZN Buy
## 3938 AMZN Buy
## 3939 AMZN Buy
## 3940 AMZN Buy
## 3941 AMZN Buy
## 3942 AMZN Buy
## 3943 AMZN Buy
## 3944 AMZN Buy
## 3945 AMZN Buy
## 3946 AMZN Buy
## 3947 AMZN Buy
## 3948 AMZN Buy
## 3949 AMZN Buy
## 3950 AMZN Buy
## 3951 AMZN Buy
## 3952 AMZN Buy
## 3953 AMZN Buy
## 3954 AMZN Buy
## 3955 AMZN Buy
## 3956 AMZN Buy
## 3957 AMZN Buy
## 3958 AMZN Buy
## 3959 AMZN Buy
## 3960 AMZN Buy
## 3961 AMZN Buy
## 3962 AMZN Buy
## 3963 AMZN Buy
## 3964 AMZN Buy
## 3965 AMZN Buy
## 3966 AMZN Buy
## 3967 AMZN Buy
## 3968 AMZN Buy
## 3969 AMZN Buy
## 3970 AMZN Buy
## 3971 AMZN Buy
## 3972 AMZN Buy
## 3973 AMZN Buy
## 3974 AMZN Buy
## 3975 AMZN Buy
## 3976 AMZN Buy
## 3977 AMZN Buy
## 3978 AMZN Buy
## 3979 AMZN Buy
## 3980 AMZN Buy
## 3981 AMZN Buy
## 3982 AMZN Buy
## 3983 AMZN Buy
## 3984 AMZN Buy
## 3985 AMZN Buy
## 3986 AMZN Buy
## 3987 AMZN Buy
## 3988 AMZN Buy
## 3989 AMZN Buy
## 3990 AMZN Buy
## 3991 AMZN Buy
## 3992 AMZN Buy
## 3993 AMZN Buy
## 3994 AMZN Buy
## 3995 AMZN Buy
## 3996 AMZN Buy
## 3997 AMZN Buy
## 3998 AMZN Buy
## 3999 AMZN Buy
## 4000 AMZN Buy
## 4001 AMZN Buy
## 4002 AMZN Buy
## 4003 AMZN Buy
## 4004 AMZN Buy
## 4005 AMZN Buy
## 4006 AMZN Buy
## 4007 AMZN Buy
## 4008 AMZN Buy
## 4009 AMZN Buy
## 4010 AMZN Buy
## 4011 AMZN Buy
## 4012 AMZN Buy
## 4013 AMZN Buy
## 4014 AMZN Buy
## 4015 AMZN Buy
## 4016 AMZN Buy
## 4017 AMZN Buy
## 4018 AMZN Buy
## 4019 AMZN Buy
## 4020 AMZN Buy
## 4021 AMZN Buy
## 4022 AMZN Buy
## 4023 AMZN Buy
## 4024 AMZN Buy
## 4025 AMZN Buy
## 4026 AMZN Buy
## 4027 AMZN Buy
## 4028 AMZN Buy
## 4029 AMZN Buy
## 4030 AMZN Buy
## 4031 AMZN Buy
## 4032 AMZN Buy
## 4033 AMZN Buy
## 4034 AMZN Buy
## 4035 AMZN Buy
## 4036 AMZN Buy
## 4037 AMZN Buy
## 4038 AMZN Buy
## 4039 AMZN Buy
## 4040 AMZN Buy
## 4041 AMZN Buy
## 4042 AMZN Buy
## 4043 AMZN Buy
## 4044 AMZN Buy
## 4045 AMZN Buy
## 4046 AMZN Buy
## 4047 AMZN Buy
## 4048 AMZN Buy
## 4049 AMZN Buy
## 4050 AMZN Buy
## 4051 AMZN Buy
## 4052 AMZN Buy
## 4053 AMZN Buy
## 4054 AMZN Buy
## 4055 AMZN Buy
## 4056 AMZN Buy
## 4057 AMZN Buy
## 4058 AMZN Buy
## 4059 AMZN Buy
## 4060 AMZN Buy
## 4061 AMZN Buy
## 4062 AMZN Buy
## 4063 AMZN Buy
## 4064 AMZN Buy
## 4065 AMZN Buy
## 4066 AMZN Buy
## 4067 AMZN Buy
## 4068 AMZN Buy
## 4069 AMZN Buy
## 4070 AMZN Buy
## 4071 AMZN Buy
## 4072 AMZN Buy
## 4073 AMZN Buy
## 4074 AMZN Buy
## 4075 AMZN Buy
## 4076 AMZN Buy
## 4077 AMZN Buy
## 4078 AMZN Buy
## 4079 AMZN Buy
## 4080 AMZN Buy
## 4081 AMZN Buy
## 4082 AMZN Buy
## 4083 AMZN Buy
## 4084 AMZN Buy
## 4085 AMZN Buy
## 4086 AMZN Buy
## 4087 AMZN Buy
## 4088 AMZN Buy
## 4089 AMZN Buy
## 4090 AMZN Buy
## 4091 AMZN Buy
## 4092 AMZN Buy
## 4093 AMZN Buy
## 4094 AMZN Buy
## 4095 AMZN Buy
## 4096 AMZN Buy
## 4097 AMZN Buy
## 4098 AMZN Buy
## 4099 AMZN Buy
## 4100 AMZN Buy
## 4101 AMZN Buy
## 4102 AMZN Buy
## 4103 AMZN Buy
## 4104 AMZN Buy
## 4105 AMZN Buy
## 4106 AMZN Buy
## 4107 AMZN Buy
## 4108 AMZN Buy
## 4109 AMZN Buy
## 4110 AMZN Buy
## 4111 AMZN Buy
## 4112 AMZN Buy
## 4113 AMZN Buy
## 4114 AMZN Buy
## 4115 AMZN Buy
## 4116 AMZN Buy
## 4117 AMZN Buy
## 4118 AMZN Buy
## 4119 AMZN Buy
## 4120 AMZN Buy
## 4121 AMZN Buy
## 4122 AMZN Buy
## 4123 AMZN Buy
## 4124 AMZN Buy
## 4125 AMZN Buy
## 4126 AMZN Buy
## 4127 AMZN Buy
## 4128 AMZN Buy
## 4129 AMZN Buy
## 4130 AMZN Buy
## 4131 AMZN Buy
## 4132 AMZN Buy
## 4133 AMZN Buy
## 4134 AMZN Buy
## 4135 AMZN Buy
## 4136 AMZN Buy
## 4137 AMZN Buy
## 4138 AMZN Buy
## 4139 AMZN Buy
## 4140 AMZN Buy
## 4141 AMZN Buy
## 4142 AMZN Buy
## 4143 AMZN Buy
## 4144 AMZN Buy
## 4145 AMZN Buy
## 4146 AMZN Buy
## 4147 AMZN Buy
## 4148 AMZN Buy
## 4149 AMZN Buy
## 4150 AMZN Buy
## 4151 AMZN Buy
## 4152 AMZN Buy
## 4153 AMZN Buy
## 4154 AMZN Buy
## 4155 AMZN Buy
## 4156 AMZN Buy
## 4157 AMZN Buy
## 4158 AMZN Buy
## 4159 AMZN Buy
## 4160 AMZN Buy
## 4161 AMZN Buy
## 4162 AMZN Buy
## 4163 AMZN Buy
## 4164 AMZN Buy
## 4165 AMZN Buy
## 4166 AMZN Buy
## 4167 AMZN Buy
## 4168 AMZN Buy
## 4169 AMZN Buy
## 4170 AMZN Buy
## 4171 AMZN Buy
## 4172 AMZN Buy
## 4173 AMZN Buy
## 4174 AMZN Buy
## 4175 AMZN Buy
## 4176 AMZN Buy
## 4177 AMZN Buy
## 4178 AMZN Buy
## 4179 AMZN Buy
## 4180 AMZN Buy
## 4181 AMZN Buy
## 4182 AMZN Buy
## 4183 AMZN Buy
## 4184 AMZN Buy
## 4185 AMZN Buy
## 4186 AMZN Buy
## 4187 AMZN Buy
## 4188 AMZN Buy
## 4189 AMZN Buy
## 4190 AMZN Buy
## 4191 AMZN Buy
## 4192 AMZN Buy
## 4193 AMZN Buy
## 4194 AMZN Buy
## 4195 AMZN Buy
## 4196 AMZN Buy
## 4197 AMZN Buy
## 4198 AMZN Buy
## 4199 AMZN Buy
## 4200 AMZN Buy
## 4201 AMZN Buy
## 4202 AMZN Buy
## 4203 AMZN Buy
## 4204 AMZN Buy
## 4205 AMZN Buy
## 4206 AMZN Buy
## 4207 AMZN Buy
## 4208 AMZN Buy
## 4209 AMZN Buy
## 4210 AMZN Buy
## 4211 AMZN Buy
## 4212 AMZN Buy
## 4213 AMZN Buy
## 4214 AMZN Buy
## 4215 AMZN Buy
## 4216 AMZN Buy
## 4217 AMZN Buy
## 4218 AMZN Buy
## 4219 AMZN Buy
## 4220 AMZN Buy
## 4221 AMZN Buy
## 4222 AMZN Buy
## 4223 AMZN Buy
## 4224 AMZN Buy
## 4225 AMZN Buy
## 4226 AMZN Buy
## 4227 AMZN Buy
## 4228 AMZN Buy
## 4229 AMZN Buy
## 4230 AMZN Buy
## 4231 AMZN Buy
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## 4233 AMZN Buy
## 4234 AMZN Buy
## 4235 AMZN Buy
## 4236 AMZN Buy
## 4237 AMZN Buy
## 4238 AMZN Buy
## 4239 AMZN Buy
## 4240 AMZN Buy
## 4241 AMZN Buy
## 4242 AMZN Buy
## 4243 AMZN Buy
## 4244 AMZN Buy
## 4245 AMZN Buy
## 4246 AMZN Buy
## 4247 AMZN Buy
## 4248 AMZN Buy
## 4249 AMZN Buy
## 4250 AMZN Buy
## 4251 AMZN Buy
## 4252 AMZN Buy
## 4253 AMZN Buy
## 4254 AMZN Buy
## 4255 AMZN Buy
## 4256 AMZN Buy
## 4257 AMZN Buy
## 4258 AMZN Buy
## 4259 AMZN Buy
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## 4261 AMZN Buy
## 4262 AMZN Buy
## 4263 AMZN Buy
## 4264 AMZN Buy
## 4265 AMZN Buy
## 4266 AMZN Buy
## 4267 AMZN Buy
## 4268 AMZN Buy
## 4269 AMZN Buy
## 4270 AMZN Buy
## 4271 AMZN Buy
## 4272 AMZN Buy
## 4273 AMZN Buy
## 4274 AMZN Buy
## 4275 AMZN Buy
## 4276 AMZN Buy
## 4277 AMZN Buy
## 4278 AMZN Buy
## 4279 AMZN Buy
## 4280 AMZN Buy
## 4281 AMZN Buy
## 4282 AMZN Buy
## 4283 AMZN Buy
## 4284 AMZN Buy
## 4285 AMZN Buy
## 4286 AMZN Buy
## 4287 AMZN Buy
## 4288 AMZN Buy
## 4289 AMZN Buy
## 4290 AMZN Buy
## 4291 AMZN Buy
## 4292 AMZN Buy
## 4293 AMZN Buy
## 4294 AMZN Buy
## 4295 AMZN Buy
## 4296 AMZN Buy
## 4297 AMZN Buy
## 4298 AMZN Buy
## 4299 AMZN Buy
## 4300 AMZN Buy
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## 4302 AMZN Buy
## 4303 AMZN Buy
## 4304 AMZN Buy
## 4305 AMZN Buy
## 4306 AMZN Buy
## 4307 AMZN Buy
## 4308 AMZN Buy
## 4309 AMZN Buy
## 4310 AMZN Buy
## 4311 AMZN Buy
## 4312 AMZN Buy
## 4313 AMZN Buy
## 4314 AMZN Buy
## 4315 AMZN Buy
## 4316 AMZN Buy
## 4317 AMZN Buy
## 4318 AMZN Buy
## 4319 AMZN Buy
## 4320 AMZN Buy
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## 4322 AMZN Buy
## 4323 AMZN Buy
## 4324 AMZN Buy
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## 4328 AMZN Buy
## 4329 AMZN Buy
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## 4334 AMZN Buy
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## 4337 AMZN Buy
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## 4342 AMZN Buy
## 4343 AMZN Buy
## 4344 AMZN Buy
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## 4346 AMZN Buy
## 4347 AMZN Buy
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## 4349 AMZN Buy
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## 4353 AMZN Buy
## 4354 AMZN Buy
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## 4356 AMZN Buy
## 4357 AMZN Buy
## 4358 AMZN Buy
## 4359 AMZN Buy
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## 4362 AMZN Buy
## 4363 AMZN Buy
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## 4365 AMZN Buy
## 4366 AMZN Buy
## 4367 AMZN Buy
## 4368 AMZN Buy
## 4369 AMZN Buy
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## 4371 AMZN Buy
## 4372 AMZN Buy
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## 4375 AMZN Buy
## 4376 AMZN Buy
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## 4383 AMZN Buy
## 4384 AMZN Buy
## 4385 AMZN Buy
## 4386 AMZN Buy
## 4387 AMZN Buy
## 4388 AMZN Buy
## 4389 AMZN Buy
## 4390 AMZN Buy
## 4391 AMZN Buy
## 4392 AMZN Buy
## 4393 AMZN Buy
## 4394 AMZN Buy
## 4395 AMZN Buy
## 4396 AMZN Buy
## 4397 AMZN Buy
## 4398 AMZN Buy
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## 4400 AMZN Buy
## 4401 AMZN Buy
## 4402 AMZN Buy
## 4403 AMZN Buy
## 4404 AMZN Buy
## 4405 AMZN Buy
## 4406 AMZN Buy
## 4407 AMZN Buy
## 4408 AMZN Buy
## 4409 AMZN Buy
## 4410 AMZN Buy
## 4411 AMZN Buy
## 4412 AMZN Buy
## 4413 AMZN Buy
## 4414 AMZN Buy
## 4415 AMZN Buy
## 4416 AMZN Buy
## 4417 AMZN Buy
## 4418 AMZN Buy
## 4419 AMZN Buy
## 4420 AMZN Buy
## 4421 AMZN Buy
## 4422 AMZN Buy
## 4423 AMZN Buy
## 4424 AMZN Buy
## 4425 AMZN Buy
## 4426 AMZN Buy
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## 4428 AMZN Buy
## 4429 AMZN Buy
## 4430 AMZN Buy
## 4431 AMZN Buy
## 4432 AMZN Buy
## 4433 AMZN Buy
## 4434 AMZN Buy
## 4435 AMZN Buy
## 4436 AMZN Buy
## 4437 AMZN Buy
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## 4441 AMZN Buy
## 4442 AMZN Buy
## 4443 AMZN Buy
## 4444 AMZN Buy
## 4445 AMZN Buy
## 4446 AMZN Buy
## 4447 AMZN Buy
## 4448 AMZN Buy
## 4449 AMZN Buy
## 4450 AMZN Buy
## 4451 AMZN Buy
## 4452 AMZN Buy
## 4453 AMZN Buy
## 4454 AMZN Buy
## 4455 AMZN Buy
## 4456 AMZN Buy
## 4457 AMZN Buy
## 4458 AMZN Buy
## 4459 AMZN Buy
## 4460 AMZN Buy
## 4461 AMZN Buy
## 4462 AMZN Buy
## 4463 AMZN Buy
## 4464 AMZN Buy
## 4465 AMZN Buy
## 4466 AMZN Buy
## 4467 AMZN Buy
## 4468 AMZN Buy
## 4469 AMZN Buy
## 4470 AMZN Buy
## 4471 AMZN Buy
## 4472 AMZN Buy
## 4473 AMZN Buy
## 4474 AMZN Buy
## 4475 AMZN Buy
## 4476 AMZN Buy
## 4477 AMZN Buy
## 4478 AMZN Buy
## 4479 AMZN Buy
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## 4481 AMZN Buy
## 4482 AMZN Buy
## 4483 AMZN Buy
## 4484 AMZN Buy
## 4485 AMZN Buy
## 4486 AMZN Buy
## 4487 AMZN Buy
## 4488 AMZN Buy
## 4489 AMZN Buy
## 4490 AMZN Buy
## 4491 AMZN Buy
## 4492 AMZN Buy
## 4493 AMZN Buy
## 4494 AMZN Buy
## 4495 AMZN Buy
## 4496 AMZN Buy
## 4497 AMZN Buy
## 4498 AMZN Buy
## 4499 AMZN Buy
## 4500 AMZN Buy
## 4501 AMZN Buy
## 4502 AMZN Buy
## 4503 AMZN Buy
## 4504 AMZN Buy
## 4505 AMZN Buy
## 4506 AMZN Buy
## 4507 AMZN Buy
## 4508 AMZN Buy
## 4509 AMZN Buy
## 4510 AMZN Buy
## 4511 AMZN Buy
## 4512 AMZN Buy
## 4513 AMZN Buy
## 4514 AMZN Buy
## 4515 AMZN Buy
## 4516 AMZN Buy
## 4517 AMZN Buy
## 4518 AMZN Buy
## 4519 AMZN Buy
## 4520 AMZN Buy
## 4521 AMZN Buy
## 4522 AMZN Buy
## 4523 AMZN Buy
## 4524 AMZN Buy
## 4525 AMZN Buy
## 4526 AMZN Buy
## 4527 AMZN Buy
## 4528 AMZN Buy
## 4529 AMZN Buy
## 4530 AMZN Buy
## 4531 AMZN Buy
## 4532 AMZN Buy
## 4533 AMZN Buy
## 4534 AMZN Buy
## 4535 AMZN Buy
## 4536 AMZN Buy
## 4537 AMZN Buy
## 4538 AMZN Buy
## 4539 AMZN Buy
## 4540 AMZN Buy
## 4541 AMZN Buy
## 4542 AMZN Buy
## 4543 AMZN Buy
## 4544 AMZN Buy
## 4545 AMZN Buy
## 4546 AMZN Buy
## 4547 AMZN Buy
## 4548 AMZN Buy
## 4549 AMZN Buy
## 4550 AMZN Buy
## 4551 AMZN Buy
## 4552 AMZN Buy
## 4553 AMZN Buy
## 4554 AMZN Buy
## 4555 AMZN Buy
## 4556 AMZN Buy
## 4557 AMZN Buy
## 4558 AMZN Buy
## 4559 AMZN Buy
## 4560 AMZN Buy
## 4561 AMZN Buy
## 4562 AMZN Buy
## 4563 AMZN Buy
## 4564 AMZN Buy
## 4565 AMZN Buy
## 4566 AMZN Buy
## 4567 AMZN Buy
## 4568 AMZN Buy
## 4569 AMZN Buy
## 4570 AMZN Buy
## 4571 AMZN Buy
## 4572 AMZN Buy
## 4573 AMZN Buy
## 4574 AMZN Buy
## 4575 AMZN Buy
## 4576 AMZN Buy
## 4577 AMZN Buy
## 4578 AMZN Buy
## 4579 AMZN Buy
## 4580 AMZN Buy
## 4581 AMZN Buy
## 4582 AMZN Buy
## 4583 AMZN Buy
## 4584 AMZN Buy
## 4585 AMZN Buy
## 4586 AMZN Buy
## 4587 AMZN Buy
## 4588 AMZN Buy
## 4589 AMZN Buy
## 4590 AMZN Buy
## 4591 AMZN Buy
## 4592 AMZN Buy
## 4593 AMZN Buy
## 4594 AMZN Buy
## 4595 AMZN Buy
## 4596 AMZN Buy
## 4597 AMZN Buy
## 4598 AMZN Buy
## 4599 AMZN Buy
## 4600 AMZN Buy
## 4601 AMZN Buy
## 4602 AMZN Buy
## 4603 AMZN Buy
## 4604 AMZN Buy
## 4605 AMZN Buy
## 4606 AMZN Buy
## 4607 AMZN Buy
## 4608 AMZN Buy
## 4609 AMZN Buy
## 4610 AMZN Buy
## 4611 AMZN Buy
## 4612 AMZN Buy
## 4613 AMZN Buy
## 4614 AMZN Buy
## 4615 AMZN Buy
## 4616 AMZN Buy
## 4617 AMZN Buy
## 4618 AMZN Buy
## 4619 AMZN Buy
## 4620 AMZN Buy
## 4621 AMZN Buy
## 4622 AMZN Buy
## 4623 AMZN Buy
## 4624 AMZN Buy
## 4625 AMZN Buy
## 4626 AMZN Buy
## 4627 AMZN Buy
## 4628 AMZN Buy
## 4629 AMZN Buy
## 4630 AMZN Buy
## 4631 AMZN Buy
## 4632 AMZN Buy
## 4633 AMZN Buy
## 4634 AMZN Buy
## 4635 AMZN Buy
## 4636 AMZN Buy
## 4637 AMZN Buy
## 4638 AMZN Buy
## 4639 AMZN Buy
## 4640 AMZN Buy
## 4641 AMZN Buy
## 4642 AMZN Buy
## 4643 AMZN Buy
## 4644 AMZN Buy
## 4645 AMZN Buy
## 4646 AMZN Buy
## 4647 AMZN Buy
## 4648 AMZN Buy
## 4649 AMZN Buy
## 4650 AMZN Buy
## 4651 AMZN Buy
## 4652 AMZN Buy
## 4653 AMZN Buy
## 4654 AMZN Buy
## 4655 AMZN Buy
## 4656 AMZN Buy
## 4657 AMZN Buy
## 4658 AMZN Buy
## 4659 AMZN Buy
## 4660 AMZN Buy
## 4661 AMZN Buy
## 4662 AMZN Buy
## 4663 AMZN Buy
## 4664 AMZN Buy
## 4665 AMZN Buy
## 4666 AMZN Buy
## 4667 AMZN Buy
## 4668 AMZN Buy
## 4669 AMZN Buy
## 4670 AMZN Buy
## 4671 AMZN Buy
## 4672 AMZN Buy
## 4673 AMZN Buy
## 4674 AMZN Buy
## 4675 AMZN Buy
## 4676 AMZN Buy
## 4677 AMZN Buy
## 4678 AMZN Buy
## 4679 AMZN Buy
## 4680 AMZN Buy
## 4681 AMZN Buy
## 4682 AMZN Buy
## 4683 AMZN Buy
## 4684 AMZN Buy
## 4685 AMZN Buy
## 4686 AMZN Buy
## 4687 AMZN Buy
## 4688 AMZN Buy
## 4689 AMZN Buy
## 4690 AMZN Buy
## 4691 AMZN Buy
## 4692 AMZN Buy
## 4693 AMZN Buy
## 4694 AMZN Buy
## 4695 AMZN Buy
## 4696 AMZN Buy
## 4697 AMZN Buy
## 4698 AMZN Buy
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## 4700 AMZN Buy
## 4701 AMZN Buy
## 4702 AMZN Buy
## 4703 AMZN Buy
## 4704 AMZN Buy
## 4705 AMZN Buy
## 4706 AMZN Buy
## 4707 AMZN Buy
## 4708 AMZN Buy
## 4709 AMZN Buy
## 4710 AMZN Buy
## 4711 AMZN Buy
## 4712 AMZN Buy
## 4713 AMZN Buy
## 4714 AMZN Buy
## 4715 AMZN Buy
## 4716 AMZN Buy
## 4717 AMZN Buy
## 4718 AMZN Buy
## 4719 AMZN Buy
## 4720 AMZN Buy
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## 4722 AMZN Buy
## 4723 AMZN Buy
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## 4725 AMZN Buy
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## 4727 AMZN Buy
## 4728 AMZN Buy
## 4729 AMZN Buy
## 4730 AMZN Buy
## 4731 AMZN Buy
## 4732 AMZN Buy
## 4733 AMZN Buy
## 4734 AMZN Buy
## 4735 AMZN Buy
## 4736 AMZN Buy
## 4737 AMZN Buy
## 4738 AMZN Buy
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## 4741 AMZN Buy
## 4742 AMZN Buy
## 4743 AMZN Buy
## 4744 AMZN Buy
## 4745 AMZN Buy
## 4746 AMZN Buy
## 4747 AMZN Buy
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## 4750 AMZN Buy
## 4751 AMZN Buy
## 4752 AMZN Buy
## 4753 AMZN Buy
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## 4755 AMZN Buy
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## 4757 AMZN Buy
## 4758 AMZN Buy
## 4759 AMZN Buy
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## 4761 AMZN Buy
## 4762 AMZN Buy
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## 4765 AMZN Buy
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## 4767 AMZN Buy
## 4768 AMZN Buy
## 4769 AMZN Buy
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## 4772 AMZN Buy
## 4773 AMZN Buy
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## 4775 AMZN Buy
## 4776 AMZN Buy
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## 4782 AMZN Buy
## 4783 AMZN Buy
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## 4785 AMZN Buy
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## 4787 AMZN Buy
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## 4790 AMZN Buy
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## 4793 AMZN Buy
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## 4796 AMZN Buy
## 4797 AMZN Buy
## 4798 AMZN Buy
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## 4801 AMZN Buy
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## 4803 AMZN Buy
## 4804 AMZN Buy
## 4805 AMZN Buy
## 4806 AMZN Buy
## 4807 AMZN Buy
## 4808 AMZN Buy
## 4809 AMZN Buy
## 4810 AMZN Buy
## 4811 AMZN Buy
## 4812 AMZN Buy
## 4813 AMZN Buy
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## 4815 AMZN Buy
## 4816 AMZN Buy
## 4817 AMZN Buy
## 4818 AMZN Buy
## 4819 AMZN Buy
## 4820 AMZN Buy
## 4821 AMZN Buy
## 4822 AMZN Buy
## 4823 AMZN Buy
## 4824 AMZN Buy
## 4825 AMZN Buy
## 4826 AMZN Buy
## 4827 AMZN Buy
## 4828 AMZN Buy
## 4829 AMZN Buy
## 4830 AMZN Buy
## 4831 AMZN Buy
## 4832 AMZN Buy
## 4833 AMZN Buy
## 4834 AMZN Buy
## 4835 AMZN Buy
## 4836 AMZN Buy
## 4837 AMZN Buy
## 4838 AMZN Buy
## 4839 AMZN Buy
## 4840 AMZN Buy
## 4841 AMZN Buy
## 4842 AMZN Buy
## 4843 AMZN Buy
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## 4845 AMZN Buy
## 4846 AMZN Buy
## 4847 AMZN Buy
## 4848 AMZN Buy
## 4849 AMZN Buy
## 4850 AMZN Buy
## 4851 AMZN Buy
## 4852 AMZN Buy
## 4853 AMZN Buy
## 4854 AMZN Buy
## 4855 AMZN Buy
## 4856 AMZN Buy
## 4857 AMZN Buy
## 4858 AMZN Buy
## 4859 AMZN Buy
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## 4861 AMZN Buy
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## 4865 AMZN Buy
## 4866 AMZN Buy
## 4867 AMZN Buy
## 4868 AMZN Buy
## 4869 AMZN Buy
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## 4872 AMZN Buy
## 4873 AMZN Buy
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## 4875 AMZN Buy
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## 4879 AMZN Buy
## 4880 AMZN Buy
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## 4882 AMZN Buy
## 4883 AMZN Buy
## 4884 AMZN Buy
## 4885 AMZN Buy
## 4886 AMZN Buy
## 4887 AMZN Buy
## 4888 AMZN Buy
## 4889 AMZN Buy
## 4890 AMZN Buy
## 4891 AMZN Buy
## 4892 AMZN Buy
## 4893 AMZN Buy
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## 4896 AMZN Buy
## 4897 AMZN Buy
## 4898 AMZN Buy
## 4899 AMZN Buy
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## 4901 AMZN Buy
## 4902 AMZN Buy
## 4903 AMZN Buy
## 4904 AMZN Buy
## 4905 AMZN Buy
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## 4907 AMZN Buy
## 4908 AMZN Buy
## 4909 AMZN Buy
## 4910 AMZN Buy
## 4911 AMZN Buy
## 4912 AMZN Buy
## 4913 AMZN Buy
## 4914 AMZN Buy
## 4915 AMZN Buy
## 4916 AMZN Buy
## 4917 AMZN Buy
## 4918 AMZN Buy
## 4919 AMZN Buy
## 4920 AMZN Buy
## 4921 AMZN Buy
## 4922 AMZN Buy
## 4923 AMZN Buy
## 4924 AMZN Buy
## 4925 AMZN Buy
## 4926 AMZN Buy
## 4927 AMZN Buy
## 4928 AMZN Buy
## 4929 AMZN Buy
## 4930 AMZN Buy
## 4931 AMZN Buy
## 4932 AMZN Buy
## 4933 AMZN Buy
## 4934 AMZN Buy
## 4935 AMZN Buy
## 4936 AMZN Buy
## 4937 AMZN Buy
## 4938 AMZN Buy
## 4939 AMZN Buy
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## 4941 AMZN Buy
## 4942 AMZN Buy
## 4943 AMZN Buy
## 4944 AMZN Buy
## 4945 AMZN Buy
## 4946 AMZN Buy
## 4947 AMZN Buy
## 4948 AMZN Buy
## 4949 AMZN Buy
## 4950 AMZN Buy
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## 4952 AMZN Buy
## 4953 AMZN Buy
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## 4955 AMZN Buy
## 4956 AMZN Buy
## 4957 AMZN Buy
## 4958 AMZN Buy
## 4959 AMZN Buy
## 4960 AMZN Buy
## 4961 AMZN Buy
## 4962 AMZN Buy
## 4963 AMZN Buy
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## 4965 AMZN Buy
## 4966 AMZN Buy
## 4967 AMZN Buy
## 4968 AMZN Buy
## 4969 AMZN Buy
## 4970 AMZN Buy
## 4971 AMZN Buy
## 4972 AMZN Buy
## 4973 AMZN Buy
## 4974 AMZN Buy
## 4975 AMZN Buy
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## 4977 AMZN Buy
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## 4980 AMZN Buy
## 4981 AMZN Buy
## 4982 AMZN Buy
## 4983 AMZN Buy
## 4984 AMZN Buy
## 4985 AMZN Buy
## 4986 AMZN Buy
## 4987 AMZN Buy
## 4988 AMZN Buy
## 4989 AMZN Buy
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## 4991 AMZN Buy
## 4992 AMZN Buy
## 4993 AMZN Buy
## 4994 AMZN Buy
## 4995 AMZN Buy
## 4996 AMZN Buy
## 4997 AMZN Buy
## 4998 AMZN Buy
## 4999 AMZN Buy
## 5000 AMZN Buy
## 5001 AMZN Buy
## 5002 AMZN Buy
## 5003 AMZN Buy
## 5004 AMZN Buy
## 5005 AMZN Buy
## 5006 AMZN Buy
## 5007 AMZN Buy
## 5008 AMZN Buy
## 5009 AMZN Buy
## 5010 AMZN Buy
## 5011 AMZN Buy
## 5012 AMZN Buy
## 5013 AMZN Buy
## 5014 AMZN Buy
## 5015 AMZN Buy
## 5016 AMZN Buy
## 5017 AMZN Buy
## 5018 AMZN Buy
## 5019 AMZN Buy
## 5020 AMZN Buy
## 5021 AMZN Buy
## 5022 AMZN Buy
## 5023 AMZN Buy
## 5024 AMZN Buy
## 5025 AMZN Buy
## 5026 AMZN Buy
## 5027 AMZN Buy
## 5028 AMZN Buy
## 5029 AMZN Buy
## 5030 AMZN Buy
## 5031 AMZN Buy
## 5032 AMZN Buy
## 5033 AMZN Buy
## 5034 AMZN Buy
## 5035 AMZN Buy
## 5036 AMZN Buy
## 5037 AMZN Buy
## 5038 AMZN Buy
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## 5041 AMZN Buy
## 5042 AMZN Buy
## 5043 AMZN Buy
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## 5045 AMZN Buy
## 5046 AMZN Buy
## 5047 AMZN Buy
## 5048 AMZN Buy
## 5049 AMZN Buy
## 5050 AMZN Buy
## 5051 AMZN Buy
## 5052 AMZN Buy
## 5053 AMZN Buy
## 5054 AMZN Buy
## 5055 AMZN Buy
## 5056 AMZN Buy
## 5057 AMZN Buy
## 5058 AMZN Buy
## 5059 AMZN Buy
## 5060 AMZN Buy
## 5061 AMZN Buy
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## 5065 AMZN Buy
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## 5067 AMZN Buy
## 5068 AMZN Buy
## 5069 AMZN Buy
## 5070 AMZN Buy
## 5071 AMZN Buy
## 5072 AMZN Buy
## 5073 AMZN Buy
## 5074 AMZN Buy
## 5075 AMZN Buy
## 5076 AMZN Buy
## 5077 AMZN Buy
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## 5080 AMZN Buy
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## 5085 AMZN Buy
## 5086 AMZN Buy
## 5087 AMZN Buy
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## 5092 AMZN Buy
## 5093 AMZN Buy
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## 5096 AMZN Buy
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## 5100 AMZN Buy
## 5101 AMZN Buy
## 5102 AMZN Buy
## 5103 AMZN Buy
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## 5105 AMZN Buy
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## 5107 AMZN Buy
## 5108 AMZN Buy
## 5109 AMZN Buy
## 5110 AMZN Buy
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## 5113 AMZN Buy
## 5114 AMZN Buy
## 5115 AMZN Buy
## 5116 AMZN Buy
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## 5125 AMZN Buy
## 5126 AMZN Buy
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## 5129 AMZN Buy
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## 5131 AMZN Buy
## 5132 AMZN Buy
## 5133 AMZN Buy
## 5134 AMZN Buy
## 5135 AMZN Buy
## 5136 AMZN Buy
## 5137 AMZN Buy
## 5138 AMZN Buy
## 5139 AMZN Buy
## 5140 AMZN Buy
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## 5142 AMZN Buy
## 5143 AMZN Buy
## 5144 AMZN Buy
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## 5146 AMZN Buy
## 5147 AMZN Buy
## 5148 AMZN Buy
## 5149 AMZN Buy
## 5150 AMZN Buy
## 5151 AMZN Buy
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## 5153 AMZN Buy
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## 5155 AMZN Buy
## 5156 AMZN Buy
## 5157 AMZN Buy
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## 5165 AMZN Buy
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## 5169 AMZN Buy
## 5170 AMZN Buy
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## 5173 AMZN Buy
## 5174 AMZN Buy
## 5175 AMZN Buy
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## 5179 AMZN Buy
## 5180 AMZN Buy
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## 5185 AMZN Buy
## 5186 AMZN Buy
## 5187 AMZN Buy
## 5188 AMZN Buy
## 5189 AMZN Buy
## 5190 AMZN Buy
## 5191 AMZN Buy
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## 5234 AMZN Buy
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## 5339 AMZN Buy
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## 5343 AMZN Buy
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## 5356 AMZN Buy
## 5357 AMZN Buy
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## 5359 AMZN Buy
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## 5361 AMZN Buy
## 5362 AMZN Buy
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## 5366 AMZN Buy
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## 5370 AMZN Buy
## 5371 AMZN Buy
## 5372 AMZN Buy
## 5373 AMZN Buy
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## 5375 AMZN Buy
## 5376 AMZN Buy
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## 5383 AMZN Buy
## 5384 AMZN Buy
## 5385 AMZN Buy
## 5386 AMZN Buy
## 5387 AMZN Buy
## 5388 AMZN Buy
## 5389 AMZN Buy
## 5390 AMZN Buy
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## 5392 AMZN Buy
## 5393 AMZN Buy
## 5394 AMZN Buy
## 5395 AMZN Buy
## 5396 AMZN Buy
## 5397 AMZN Buy
## 5398 AMZN Buy
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## 5400 AMZN Buy
## 5401 AMZN Buy
## 5402 AMZN Buy
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## 5404 AMZN Buy
## 5405 AMZN Buy
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## 5442 AMZN Buy
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## 5444 AMZN Buy
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## 5447 AMZN Buy
## 5448 AMZN Buy
## 5449 AMZN Buy
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## 5452 AMZN Buy
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## 5454 AMZN Buy
## 5455 AMZN Buy
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## 5457 AMZN Buy
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## 5459 AMZN Buy
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## 5461 AMZN Buy
## 5462 AMZN Buy
## 5463 AMZN Buy
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## 5470 AMZN Buy
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## 5472 AMZN Buy
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## 5474 AMZN Buy
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## 5476 AMZN Buy
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## 5478 AMZN Buy
## 5479 AMZN Buy
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## 5481 AMZN Buy
## 5482 AMZN Buy
## 5483 AMZN Buy
## 5484 AMZN Buy
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## 5487 AMZN Buy
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## 5489 AMZN Buy
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## 5491 AMZN Buy
## 5492 AMZN Buy
## 5493 AMZN Buy
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## 5496 AMZN Buy
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## 5500 AMZN Buy
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## 5502 AMZN Buy
## 5503 AMZN Buy
## 5504 AMZN Buy
## 5505 AMZN Buy
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## 5507 AMZN Buy
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## 5517 AMZN Buy
## 5518 AMZN Buy
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## 5520 AMZN Buy
## 5521 AMZN Buy
## 5522 AMZN Buy
## 5523 AMZN Buy
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## 5525 AMZN Buy
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## 5534 AMZN Buy
## 5535 AMZN Buy
## 5536 AMZN Buy
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## 5545 AMZN Buy
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## 5549 AMZN Buy
## 5550 AMZN Buy
## 5551 AMZN Buy
## 5552 AMZN Buy
## 5553 AMZN Buy
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## 5555 AMZN Buy
## 5556 AMZN Buy
## 5557 AMZN Buy
## 5558 AMZN Buy
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## 5561 AMZN Buy
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## 5563 AMZN Buy
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## 5565 AMZN Buy
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## 5568 AMZN Buy
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## 5570 AMZN Buy
## 5571 AMZN Buy
## 5572 AMZN Buy
## 5573 AMZN Buy
## 5574 AMZN Buy
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## 5576 AMZN Buy
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## 5578 AMZN Buy
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## 5588 AMZN Buy
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## 5590 AMZN Buy
## 5591 AMZN Buy
## 5592 AMZN Buy
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## 5596 AMZN Buy
## 5597 AMZN Buy
## 5598 AMZN Buy
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## 5601 AMZN Buy
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## 5603 AMZN Buy
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## 5639 AMZN Buy
## 5640 AMZN Buy
## 5641 AMZN Buy
## 5642 AMZN Buy
## 5643 AMZN Buy
## 5644 AMZN Buy
## 5645 AMZN Buy
## 5646 AMZN Buy
## 5647 AMZN Buy
## 5648 AMZN Buy
## 5649 AMZN Buy
## 5650 AMZN Buy
## 5651 AMZN Buy
## 5652 AMZN Buy
## 5653 AMZN Buy
## 5654 AMZN Buy
## 5655 AMZN Buy
## 5656 AMZN Buy
## 5657 AMZN Buy
## 5658 AMZN Buy
## 5659 AMZN Buy
## 5660 AMZN Buy
## 5661 AMZN Buy
## 5662 AMZN Buy
## 5663 AMZN Buy
## 5664 AMZN Buy
## 5665 AMZN Buy
## 5666 AMZN Buy
## 5667 AMZN Buy
## 5668 AMZN Buy
## 5669 AMZN Buy
## 5670 AMZN Buy
## 5671 AMZN Buy
## 5672 AMZN Buy
## 5673 AMZN Buy
## 5674 AMZN Buy
## 5675 AMZN Buy
## 5676 AMZN Buy
## 5677 AMZN Buy
## 5678 AMZN Buy
## 5679 AMZN Buy
## 5680 AMZN Buy
## 5681 AMZN Buy
## 5682 AMZN Buy
## 5683 AMZN Buy
## 5684 AMZN Buy
## 5685 AMZN Buy
## 5686 AMZN Buy
## 5687 AMZN Buy
## 5688 AMZN Buy
## 5689 AMZN Buy
## 5690 AMZN Buy
## 5691 AMZN Buy
## 5692 AMZN Buy
## 5693 AMZN Buy
## 5694 AMZN Buy
## 5695 AMZN Buy
## 5696 AMZN Buy
## 5697 AMZN Buy
## 5698 AMZN Buy
## 5699 AMZN Buy
## 5700 AMZN Buy
## 5701 AMZN Buy
## 5702 AMZN Buy
## 5703 AMZN Buy
## 5704 AMZN Buy
## 5705 AMZN Buy
## 5706 AMZN Buy
## 5707 AMZN Buy
## 5708 AMZN Buy
## 5709 AMZN Buy
## 5710 AMZN Buy
## 5711 AMZN Buy
## 5712 AMZN Buy
## 5713 AMZN Buy
## 5714 AMZN Buy
## 5715 AMZN Buy
## 5716 AMZN Buy
## 5717 AMZN Buy
## 5718 AMZN Buy
## 5719 AMZN Buy
## 5720 AMZN Buy
## 5721 AMZN Buy
## 5722 AMZN Buy
## 5723 AMZN Buy
## 5724 AMZN Buy
## 5725 AMZN Buy
## 5726 AMZN Buy
## 5727 AMZN Buy
## 5728 AMZN Buy
## 5729 AMZN Buy
## 5730 AMZN Buy
## 5731 AMZN Buy
## 5732 AMZN Buy
## 5733 AMZN Buy
## 5734 AMZN Buy
## 5735 AMZN Buy
## 5736 AMZN Buy
## 5737 AMZN Buy
## 5738 AMZN Buy
## 5739 AMZN Buy
## 5740 AMZN Buy
## 5741 AMZN Buy
## 5742 AMZN Buy
## 5743 AMZN Buy
## 5744 AMZN Buy
## 5745 AMZN Buy
## 5746 AMZN Buy
## 5747 AMZN Buy
## 5748 AMZN Buy
## 5749 AMZN Buy
## 5750 AMZN Buy
## 5751 AMZN Buy
## 5752 AMZN Buy
## 5753 AMZN Buy
## 5754 AMZN Buy
## 5755 AMZN Buy
## 5756 AMZN Buy
## 5757 AMZN Buy
## 5758 AMZN Buy
## 5759 AMZN Buy
## 5760 AMZN Buy
## 5761 AMZN Buy
## 5762 AMZN Buy
## 5763 AMZN Buy
## 5764 AMZN Buy
## 5765 AMZN Buy
## 5766 AMZN Buy
## 5767 AMZN Buy
## 5768 AMZN Buy
## 5769 AMZN Buy
## 5770 AMZN Buy
## 5771 AMZN Buy
## 5772 AMZN Buy
## 5773 AMZN Buy
## 5774 AMZN Buy
## 5775 AMZN Buy
## 5776 AMZN Buy
## 5777 AMZN Buy
## 5778 AMZN Buy
## 5779 AMZN Buy
## 5780 AMZN Buy
## 5781 AMZN Buy
## 5782 AMZN Buy
## 5783 AMZN Buy
## 5784 AMZN Buy
## 5785 AMZN Buy
## 5786 AMZN Buy
## 5787 AMZN Buy
## 5788 AMZN Buy
## 5789 AMZN Buy
## 5790 AMZN Buy
## 5791 AMZN Buy
## 5792 AMZN Buy
## 5793 AMZN Buy
## 5794 AMZN Buy
## 5795 AMZN Buy
## 5796 AMZN Buy
## 5797 AMZN Buy
## 5798 AMZN Buy
## 5799 AMZN Buy
## 5800 AMZN Buy
## 5801 AMZN Buy
## 5802 AMZN Buy
## 5803 AMZN Buy
## 5804 AMZN Buy
## 5805 AMZN Buy
## 5806 AMZN Buy
## 5807 AMZN Buy
## 5808 AMZN Buy
## 5809 AMZN Buy
## 5810 AMZN Buy
## 5811 AMZN Buy
## 5812 AMZN Buy
## 5813 AMZN Buy
## 5814 AMZN Buy
## 5815 AMZN Buy
## 5816 AMZN Buy
## 5817 AMZN Buy
## 5818 AMZN Buy
## 5819 AMZN Buy
## 5820 AMZN Buy
## 5821 AMZN Buy
## 5822 AMZN Buy
## 5823 AMZN Buy
## 5824 AMZN Buy
## 5825 AMZN Buy
## 5826 AMZN Buy
## 5827 AMZN Buy
## 5828 AMZN Buy
## 5829 AMZN Buy
## 5830 AMZN Buy
## 5831 AMZN Buy
## 5832 AMZN Buy
## 5833 AMZN Buy
## 5834 AMZN Buy
## 5835 AMZN Buy
## 5836 AMZN Buy
## 5837 AMZN Buy
## 5838 AMZN Buy
## 5839 AMZN Buy
## 5840 AMZN Buy
## 5841 AMZN Buy
## 5842 AMZN Buy
## 5843 AMZN Buy
## 5844 AMZN Buy
## 5845 AMZN Buy
## 5846 AMZN Buy
## 5847 AMZN Buy
## 5848 AMZN Buy
## 5849 AMZN Buy
## 5850 AMZN Buy
## 5851 AMZN Buy
## 5852 AMZN Buy
## 5853 AMZN Buy
## 5854 AMZN Buy
## 5855 AMZN Buy
## 5856 AMZN Buy
## 5857 AMZN Buy
## 5858 AMZN Buy
## 5859 AMZN Buy
## 5860 AMZN Buy
## 5861 AMZN Buy
## 5862 AMZN Buy
## 5863 AMZN Buy
## 5864 AMZN Buy
## 5865 AMZN Buy
## 5866 AMZN Buy
## 5867 AMZN Buy
## 5868 AMZN Buy
## 5869 AMZN Buy
## 5870 AMZN Buy
## 5871 AMZN Buy
## 5872 AMZN Buy
## 5873 AMZN Buy
## 5874 AMZN Buy
## 5875 AMZN Buy
## 5876 AMZN Buy
## 5877 AMZN Buy
## 5878 AMZN Buy
## 5879 AMZN Buy
## 5880 AMZN Buy
## 5881 AMZN Buy
## 5882 AMZN Buy
## 5883 AMZN Buy
## 5884 AMZN Buy
## 5885 AMZN Buy
## 5886 AMZN Buy
## 5887 AMZN Buy
## 5888 AMZN Buy
## 5889 AMZN Buy
## 5890 AMZN Buy
## 5891 AMZN Buy
## 5892 AMZN Buy
## 5893 AMZN Buy
## 5894 AMZN Buy
## 5895 AMZN Buy
## 5896 AMZN Buy
## 5897 AMZN Buy
## 5898 AMZN Buy
## 5899 AMZN Buy
## 5900 AMZN Buy
## 5901 AMZN Buy
## 5902 AMZN Buy
## 5903 AMZN Buy
## 5904 AMZN Buy
## 5905 AMZN Buy
## 5906 AMZN Buy
## 5907 AMZN Buy
## 5908 AMZN Buy
## 5909 AMZN Buy
## 5910 AMZN Buy
## 5911 AMZN Buy
## 5912 AMZN Buy
## 5913 AMZN Buy
## 5914 AMZN Buy
## 5915 AMZN Buy
## 5916 AMZN Buy
## 5917 AMZN Buy
## 5918 AMZN Buy
## 5919 AMZN Buy
## 5920 AMZN Buy
## 5921 AMZN Buy
## 5922 AMZN Buy
## 5923 AMZN Buy
## 5924 AMZN Buy
## 5925 AMZN Buy
## 5926 AMZN Buy
## 5927 AMZN Buy
## 5928 AMZN Buy
## 5929 AMZN Buy
## 5930 AMZN Buy
## 5931 AMZN Buy
## 5932 AMZN Buy
## 5933 AMZN Buy
## 5934 AMZN Buy
## 5935 AMZN Buy
## 5936 AMZN Buy
## 5937 AMZN Buy
## 5938 AMZN Buy
## 5939 AMZN Buy
## 5940 AMZN Buy
## 5941 AMZN Buy
## 5942 AMZN Buy
## 5943 AMZN Buy
## 5944 AMZN Buy
## 5945 AMZN Buy
## 5946 AMZN Buy
## 5947 AMZN Buy
## 5948 AMZN Buy
## 5949 AMZN Buy
## 5950 AMZN Buy
## 5951 AMZN Buy
## 5952 AMZN Buy
## 5953 AMZN Buy
## 5954 AMZN Buy
## 5955 AMZN Buy
## 5956 AMZN Buy
## 5957 AMZN Buy
## 5958 AMZN Buy
## 5959 AMZN Buy
## 5960 AMZN Buy
## 5961 AMZN Buy
## 5962 AMZN Buy
## 5963 AMZN Buy
## 5964 AMZN Buy
## 5965 AMZN Buy
## 5966 AMZN Buy
## 5967 AMZN Buy
## 5968 AMZN Buy
## 5969 AMZN Buy
## 5970 AMZN Buy
## 5971 AMZN Buy
## 5972 AMZN Buy
## 5973 AMZN Buy
## 5974 AMZN Buy
## 5975 AMZN Buy
## 5976 AMZN Buy
## 5977 AMZN Buy
## 5978 AMZN Buy
## 5979 AMZN Buy
## 5980 AMZN Buy
## 5981 AMZN Buy
## 5982 AMZN Buy
## 5983 AMZN Buy
## 5984 AMZN Buy
## 5985 AMZN Buy
## 5986 AMZN Buy
## 5987 AMZN Buy
## 5988 AMZN Buy
## 5989 AMZN Buy
## 5990 AMZN Buy
## 5991 AMZN Buy
## 5992 AMZN Buy
## 5993 AMZN Buy
## 5994 AMZN Buy
## 5995 AMZN Buy
## 5996 AMZN Buy
## 5997 AMZN Buy
## 5998 AMZN Buy
## 5999 AMZN Buy
## 6000 AMZN Buy
## 6001 AMZN Buy
## 6002 AMZN Buy
## 6003 AMZN Buy
## 6004 AMZN Buy
## 6005 AMZN Buy
## 6006 AMZN Buy
## 6007 AMZN Buy
## 6008 AMZN Buy
## 6009 AMZN Buy
## 6010 AMZN Buy
## 6011 AMZN Buy
## 6012 AMZN Buy
## 6013 AMZN Buy
## 6014 AMZN Buy
## 6015 AMZN Buy
## 6016 AMZN Buy
## 6017 AMZN Buy
## 6018 AMZN Buy
## 6019 AMZN Buy
## 6020 AMZN Buy
## 6021 AMZN Buy
## 6022 AMZN Buy
## 6023 AMZN Buy
## 6024 AMZN Buy
## 6025 AMZN Buy
## 6026 AMZN Buy
## 6027 AMZN Buy
## 6028 AMZN Buy
## 6029 AMZN Buy
## 6030 AMZN Buy
## 6031 AMZN Buy
## 6032 AMZN Buy
## 6033 AMZN Buy
## 6034 AMZN Buy
## 6035 AMZN Buy
## 6036 AMZN Buy
## 6037 AMZN Buy
## 6038 AMZN Buy
## 6039 AMZN Buy
## 6040 AMZN Buy
## 6041 AMZN Buy
## 6042 AMZN Buy
## 6043 AMZN Buy
## 6044 AMZN Buy
## 6045 AMZN Buy
## 6046 AMZN Buy
## 6047 AMZN Buy
## 6048 AMZN Buy
## 6049 AMZN Buy
## 6050 AMZN Buy
## 6051 AMZN Buy
## 6052 AMZN Buy
## 6053 AMZN Buy
## 6054 AMZN Buy
## 6055 AMZN Buy
## 6056 AMZN Buy
## 6057 AMZN Buy
## 6058 AMZN Buy
## 6059 AMZN Buy
## 6060 AMZN Buy
## 6061 AMZN Buy
## 6062 AMZN Buy
## 6063 AMZN Buy
## 6064 AMZN Buy
## 6065 AMZN Buy
## 6066 AMZN Buy
## 6067 AMZN Buy
## 6068 AMZN Buy
## 6069 AMZN Buy
## 6070 AMZN Buy
## 6071 AMZN Buy
## 6072 AMZN Buy
## 6073 AMZN Buy
## 6074 AMZN Buy
## 6075 AMZN Buy
## 6076 AMZN Buy
## 6077 AMZN Buy
## 6078 AMZN Buy
## 6079 AMZN Buy
## 6080 AMZN Buy
## 6081 AMZN Buy
## 6082 AMZN Buy
## 6083 AMZN Buy
## 6084 AMZN Buy
## 6085 AMZN Buy
## 6086 AMZN Buy
## 6087 AMZN Buy
## 6088 AMZN Buy
## 6089 AMZN Buy
## 6090 AMZN Buy
## 6091 AMZN Buy
## 6092 AMZN Buy
## 6093 AMZN Buy
## 6094 AMZN Buy
## 6095 AMZN Buy
## 6096 AMZN Buy
## 6097 AMZN Buy
## 6098 AMZN Buy
## 6099 AMZN Buy
## 6100 AMZN Buy
## 6101 AMZN Buy
## 6102 AMZN Buy
## 6103 AMZN Buy
## 6104 AMZN Buy
## 6105 AMZN Buy
## 6106 AMZN Buy
## 6107 AMZN Buy
## 6108 AMZN Buy
## 6109 AMZN Buy
## 6110 AMZN Buy
## 6111 AMZN Buy
## 6112 AMZN Buy
## 6113 AMZN Buy
## 6114 AMZN Buy
## 6115 AMZN Buy
## 6116 AMZN Buy
## 6117 AMZN Buy
## 6118 AMZN Buy
## 6119 AMZN Buy
## 6120 AMZN Buy
## 6121 AMZN Buy
## 6122 AMZN Buy
## 6123 AMZN Buy
## 6124 AMZN Buy
## 6125 AMZN Buy
## 6126 AMZN Buy
## 6127 AMZN Buy
## 6128 AMZN Buy
## 6129 AMZN Buy
## 6130 AMZN Buy
## 6131 AMZN Buy
## 6132 AMZN Buy
## 6133 AMZN Buy
## 6134 AMZN Buy
## 6135 AMZN Buy
## 6136 AMZN Buy
## 6137 AMZN Buy
## 6138 AMZN Buy
## 6139 AMZN Buy
## 6140 AMZN Buy
## 6141 AMZN Buy
## 6142 AMZN Buy
## 6143 AMZN Buy
## 6144 AMZN Buy
## 6145 AMZN Buy
## 6146 AMZN Buy
## 6147 AMZN Buy
## 6148 AMZN Buy
## 6149 AMZN Buy
## 6150 AMZN Buy
## 6151 AMZN Buy
## 6152 AMZN Buy
## 6153 AMZN Buy
## 6154 AMZN Buy
## 6155 AMZN Buy
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## 6157 AMZN Buy
## 6158 AMZN Buy
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## 6160 AMZN Buy
## 6161 AMZN Buy
## 6162 AMZN Buy
## 6163 AMZN Buy
## 6164 AMZN Buy
## 6165 AMZN Buy
## 6166 AMZN Buy
## 6167 AMZN Buy
## 6168 AMZN Buy
## 6169 AMZN Buy
## 6170 AMZN Buy
## 6171 AMZN Buy
## 6172 AMZN Buy
## 6173 AMZN Buy
## 6174 AMZN Buy
## 6175 AMZN Buy
## 6176 AMZN Buy
## 6177 AMZN Buy
## 6178 AMZN Buy
## 6179 AMZN Buy
## 6180 AMZN Buy
## 6181 AMZN Buy
## 6182 AMZN Buy
## 6183 AMZN Buy
## 6184 AMZN Buy
## 6185 AMZN Buy
## 6186 AMZN Buy
## 6187 AMZN Buy
## 6188 AMZN Buy
## 6189 AMZN Buy
## 6190 AMZN Buy
## 6191 AMZN Buy
## 6192 AMZN Buy
## 6193 AMZN Buy
## 6194 AMZN Buy
## 6195 AMZN Buy
## 6196 AMZN Buy
## 6197 AMZN Buy
## 6198 AMZN Buy
## 6199 AMZN Buy
## 6200 AMZN Buy
## 6201 AMZN Buy
## 6202 AMZN Buy
## 6203 AMZN Buy
## 6204 AMZN Buy
## 6205 AMZN Buy
## 6206 AMZN Buy
## 6207 AMZN Buy
## 6208 AMZN Buy
## 6209 AMZN Buy
## 6210 AMZN Buy
## 6211 AMZN Buy
## 6212 AMZN Buy
## 6213 AMZN Buy
## 6214 AMZN Buy
## 6215 AMZN Buy
## 6216 AMZN Buy
## 6217 AMZN Buy
## 6218 AMZN Buy
## 6219 AMZN Buy
## 6220 AMZN Buy
## 6221 AMZN Buy
## 6222 AMZN Buy
## 6223 AMZN Buy
## 6224 AMZN Buy
## 6225 AMZN Buy
## 6226 AMZN Buy
## 6227 AMZN Buy
## 6228 AMZN Buy
## 6229 AMZN Buy
## 6230 AMZN Buy
## 6231 AMZN Buy
## 6232 AMZN Buy
## 6233 AMZN Buy
## 6234 AMZN Buy
## 6235 AMZN Buy
## 6236 AMZN Buy
## 6237 AMZN Buy
## 6238 AMZN Buy
## 6239 AMZN Buy
## 6240 AMZN Buy
## 6241 AMZN Buy
## 6242 AMZN Buy
## 6243 AMZN Buy
## 6244 AMZN Buy
## 6245 AMZN Buy
## 6246 AMZN Buy
## 6247 AMZN Buy
## 6248 AMZN Buy
## 6249 AMZN Buy
## 6250 AMZN Buy
## 6251 AMZN Buy
## 6252 AMZN Buy
## 6253 AMZN Buy
## 6254 AMZN Buy
## 6255 AMZN Buy
## 6256 AMZN Buy
## 6257 AMZN Buy
## 6258 AMZN Buy
## 6259 AMZN Buy
## 6260 AMZN Buy
## 6261 AMZN Buy
## 6262 AMZN Buy
## 6263 AMZN Buy
## 6264 AMZN Buy
## 6265 AMZN Buy
## 6266 AMZN Buy
## 6267 AMZN Buy
## 6268 AMZN Buy
## 6269 AMZN Buy
## 6270 AMZN Buy
## 6271 AMZN Buy
## 6272 AMZN Buy
## 6273 AMZN Buy
## 6274 AMZN Buy
## 6275 AMZN Buy
## 6276 AMZN Buy
## 6277 AMZN Buy
## 6278 AMZN Buy
## 6279 AMZN Buy
## 6280 AMZN Buy
## 6281 AMZN Buy
## 6282 AMZN Buy
## 6283 AMZN Buy
## 6284 AMZN Buy
## 6285 AMZN Buy
## 6286 AMZN Buy
## 6287 AMZN Buy
## 6288 AMZN Buy
## 6289 AMZN Buy
## 6290 AMZN Buy
## 6291 AMZN Buy
## 6292 AMZN Buy
## 6293 AMZN Buy
## 6294 AMZN Buy
## 6295 AMZN Buy
## 6296 AMZN Buy
## 6297 AMZN Buy
## 6298 AMZN Buy
## 6299 AMZN Buy
## 6300 AMZN Buy
## 6301 AMZN Buy
## 6302 AMZN Buy
## 6303 AMZN Buy
## 6304 AMZN Buy
## 6305 AMZN Buy
## 6306 AMZN Buy
## 6307 AMZN Buy
## 6308 AMZN Buy
## 6309 AMZN Buy
## 6310 AMZN Buy
## 6311 AMZN Buy
## 6312 AMZN Buy
## 6313 AMZN Buy
## 6314 AMZN Buy
## 6315 AMZN Buy
## 6316 AMZN Buy
## 6317 AMZN Buy
## 6318 AMZN Buy
## 6319 AMZN Buy
## 6320 AMZN Buy
## 6321 AMZN Buy
## 6322 AMZN Buy
## 6323 AMZN Buy
## 6324 AMZN Buy
## 6325 AMZN Buy
## 6326 AMZN Buy
## 6327 AMZN Buy
## 6328 AMZN Buy
## 6329 AMZN Buy
## 6330 AMZN Buy
## 6331 AMZN Buy
## 6332 AMZN Buy
## 6333 AMZN Buy
## 6334 AMZN Buy
## 6335 AMZN Buy
## 6336 AMZN Buy
## 6337 AMZN Buy
## 6338 AMZN Buy
## 6339 AMZN Buy
## 6340 AMZN Buy
## 6341 AMZN Buy
## 6342 AMZN Buy
## 6343 AMZN Buy
## 6344 AMZN Buy
## 6345 AMZN Buy
## 6346 AMZN Buy
## 6347 AMZN Buy
## 6348 AMZN Buy
## 6349 AMZN Buy
## 6350 AMZN Buy
## 6351 AMZN Buy
## 6352 AMZN Buy
## 6353 AMZN Buy
## 6354 AMZN Buy
## 6355 AMZN Buy
## 6356 AMZN Buy
## 6357 AMZN Buy
## 6358 AMZN Buy
## 6359 AMZN Buy
## 6360 AMZN Buy
## 6361 AMZN Buy
## 6362 AMZN Buy
## 6363 AMZN Buy
## 6364 AMZN Buy
## 6365 AMZN Buy
## 6366 AMZN Buy
## 6367 AMZN Buy
## 6368 AMZN Buy
## 6369 AMZN Buy
## 6370 AMZN Buy
## 6371 AMZN Buy
## 6372 AMZN Buy
## 6373 AMZN Buy
## 6374 AMZN Buy
## 6375 AMZN Buy
## 6376 AMZN Buy
## 6377 AMZN Buy
## 6378 AMZN Buy
## 6379 AMZN Buy
## 6380 AMZN Buy
## 6381 AMZN Buy
## 6382 AMZN Buy
## 6383 AMZN Buy
## 6384 AMZN Buy
## 6385 AMZN Buy
## 6386 AMZN Buy
## 6387 AMZN Buy
## 6388 AMZN Buy
## 6389 AMZN Buy
## 6390 AMZN Buy
## 6391 AMZN Buy
## 6392 AMZN Buy
## 6393 AMZN Buy
## 6394 AMZN Buy
## 6395 AMZN Buy
## 6396 AMZN Buy
## 6397 AMZN Buy
## 6398 AMZN Buy
## 6399 AMZN Buy
## 6400 AMZN Buy
## 6401 AMZN Buy
## 6402 AMZN Buy
## 6403 AMZN Buy
## 6404 AMZN Buy
## 6405 AMZN Buy
## 6406 AMZN Buy
## 6407 AMZN Buy
## 6408 AMZN Buy
## 6409 AMZN Buy
## 6410 AMZN Buy
## 6411 AMZN Buy
## 6412 AMZN Buy
## 6413 AMZN Buy
## 6414 AMZN Buy
## 6415 AMZN Buy
## 6416 AMZN Buy
## 6417 AMZN Buy
## 6418 AMZN Buy
## 6419 AMZN Buy
## 6420 AMZN Buy
## 6421 AMZN Buy
## 6422 AMZN Buy
## 6423 AMZN Buy
## 6424 AMZN Buy
## 6425 AMZN Buy
## 6426 AMZN Buy
## 6427 AMZN Buy
## 6428 AMZN Buy
## 6429 AMZN Buy
## 6430 AMZN Buy
## 6431 AMZN Buy
## 6432 AMZN Buy
## 6433 AMZN Buy
## 6434 AMZN Buy
## 6435 AMZN Buy
## 6436 AMZN Buy
## 6437 AMZN Buy
## 6438 AMZN Buy
## 6439 AMZN Buy
## 6440 AMZN Buy
## 6441 AMZN Buy
## 6442 AMZN Buy
## 6443 AMZN Buy
## 6444 AMZN Buy
## 6445 AMZN Buy
## 6446 AMZN Buy
## 6447 AMZN Buy
## 6448 AMZN Buy
## 6449 AMZN Buy
## 6450 AMZN Buy
## 6451 AMZN Buy
## 6452 AMZN Buy
## 6453 AMZN Buy
## 6454 AMZN Buy
## 6455 AMZN Buy
## 6456 AMZN Buy
## 6457 AMZN Buy
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## 6459 AMZN Buy
## 6460 AMZN Buy
## 6461 AMZN Buy
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## 6466 AMZN Buy
## 6467 AMZN Buy
## 6468 AMZN Buy
## 6469 AMZN Buy
## 6470 AMZN Buy
## 6471 AMZN Buy
## 6472 AMZN Buy
## 6473 AMZN Buy
## 6474 AMZN Buy
## 6475 AMZN Buy
## 6476 AMZN Buy
## 6477 AMZN Buy
## 6478 AMZN Buy
## 6479 AMZN Buy
## 6480 AMZN Buy
## 6481 AMZN Buy
## 6482 AMZN Buy
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## 6487 AMZN Buy
## 6488 AMZN Buy
## 6489 AMZN Buy
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## 6491 AMZN Buy
## 6492 AMZN Buy
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## 6494 AMZN Buy
## 6495 AMZN Buy
## 6496 AMZN Buy
## 6497 AMZN Buy
## 6498 AMZN Buy
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## 6500 AMZN Buy
## 6501 AMZN Buy
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## 6507 AMZN Buy
## 6508 AMZN Buy
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## 6510 AMZN Buy
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## 6512 AMZN Buy
## 6513 AMZN Buy
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## 6516 AMZN Buy
## 6517 AMZN Buy
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## 6519 AMZN Buy
## 6520 AMZN Buy
## 6521 AMZN Buy
## 6522 AMZN Buy
## 6523 AMZN Buy
## 6524 AMZN Buy
## 6525 AMZN Buy
## 6526 AMZN Buy
## 6527 AMZN Buy
## 6528 AMZN Buy
## 6529 AMZN Buy
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## 6532 AMZN Buy
## 6533 AMZN Buy
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## 6535 AMZN Buy
## 6536 AMZN Buy
## 6537 AMZN Buy
## 6538 AMZN Buy
## 6539 AMZN Buy
## 6540 AMZN Buy
## 6541 AMZN Buy
## 6542 AMZN Buy
## 6543 JNJ Sell
## 6544 JNJ Sell
## 6545 JNJ Sell
## 6546 JNJ Sell
## 6547 JNJ Buy
## 6548 JNJ Buy
## 6549 JNJ Buy
## 6550 JNJ Buy
## 6551 JNJ Buy
## 6552 JNJ Buy
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## 6554 JNJ Buy
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## 6556 JNJ Buy
## 6557 JNJ Buy
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## 6561 JNJ Buy
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## 6690 JNJ Buy
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## 6702 JNJ Buy
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## 6709 JNJ Buy
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## 6863 JNJ Buy
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## 6871 JNJ Buy
## 6872 JNJ Buy
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## 6874 JNJ Buy
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## 6876 JNJ Buy
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## 6957 JNJ Buy
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## 6990 JNJ Buy
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## 6999 JNJ Buy
## 7000 JNJ Buy
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## 7035 JNJ Buy
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## 7051 JNJ Buy
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## 7155 JNJ Buy
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## 7190 JNJ Buy
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## 7192 JNJ Buy
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## 7200 JNJ Buy
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## 7203 JNJ Buy
## 7204 JNJ Buy
## 7205 JNJ Buy
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## 7209 JNJ Buy
## 7210 JNJ Buy
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## 7212 JNJ Buy
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## 7214 JNJ Buy
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## 7218 JNJ Buy
## 7219 JNJ Buy
## 7220 JNJ Buy
## 7221 JNJ Buy
## 7222 JNJ Buy
## 7223 JNJ Buy
## 7224 JNJ Buy
## 7225 JNJ Buy
## 7226 JNJ Buy
## 7227 JNJ Buy
## 7228 JNJ Buy
## 7229 JNJ Buy
## 7230 JNJ Buy
## 7231 JNJ Buy
## 7232 JNJ Buy
## 7233 JNJ Buy
## 7234 JNJ Buy
## 7235 JNJ Buy
## 7236 JNJ Buy
## 7237 JNJ Buy
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## 7239 JNJ Buy
## 7240 JNJ Buy
## 7241 JNJ Buy
## 7242 JNJ Buy
## 7243 JNJ Buy
## 7244 JNJ Buy
## 7245 JNJ Buy
## 7246 JNJ Buy
## 7247 JNJ Buy
## 7248 JNJ Buy
## 7249 JNJ Buy
## 7250 JNJ Buy
## 7251 JNJ Buy
## 7252 JNJ Buy
## 7253 JNJ Buy
## 7254 JNJ Buy
## 7255 JNJ Buy
## 7256 JNJ Buy
## 7257 JNJ Buy
## 7258 JNJ Buy
## 7259 JNJ Buy
## 7260 JNJ Buy
## 7261 JNJ Buy
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## 7263 JNJ Buy
## 7264 JNJ Buy
## 7265 JNJ Buy
## 7266 JNJ Buy
## 7267 JNJ Buy
## 7268 JNJ Buy
## 7269 JNJ Buy
## 7270 JNJ Buy
## 7271 JNJ Buy
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## 7273 JNJ Buy
## 7274 JNJ Buy
## 7275 JNJ Buy
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## 7279 JNJ Buy
## 7280 JNJ Buy
## 7281 JNJ Buy
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## 7283 JNJ Buy
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## 7285 JNJ Buy
## 7286 JNJ Buy
## 7287 JNJ Buy
## 7288 JNJ Buy
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## 7290 JNJ Buy
## 7291 JNJ Buy
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## 7294 JNJ Buy
## 7295 JNJ Buy
## 7296 JNJ Buy
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## 7298 JNJ Buy
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## 7300 JNJ Buy
## 7301 JNJ Buy
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## 7303 JNJ Buy
## 7304 JNJ Buy
## 7305 JNJ Buy
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## 7310 JNJ Buy
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## 7319 JNJ Buy
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## 7326 JNJ Buy
## 7327 JNJ Buy
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## 7329 JNJ Buy
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## 7331 JNJ Buy
## 7332 JNJ Buy
## 7333 JNJ Buy
## 7334 JNJ Buy
## 7335 JNJ Buy
## 7336 JNJ Buy
## 7337 JNJ Buy
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## 7339 JNJ Buy
## 7340 JNJ Buy
## 7341 JNJ Buy
## 7342 JNJ Buy
## 7343 JNJ Buy
## 7344 JNJ Buy
## 7345 JNJ Buy
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## 7349 JNJ Buy
## 7350 JNJ Buy
## 7351 JNJ Buy
## 7352 JNJ Buy
## 7353 JNJ Buy
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## 7355 JNJ Buy
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## 7357 JNJ Buy
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## 7359 JNJ Buy
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## 7361 JNJ Buy
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## 7364 JNJ Buy
## 7365 JNJ Buy
## 7366 JNJ Buy
## 7367 JNJ Buy
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## 7370 JNJ Buy
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## 7373 JNJ Buy
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## 7375 JNJ Buy
## 7376 JNJ Buy
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## 7381 JNJ Buy
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## 7384 JNJ Buy
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## 7386 JNJ Buy
## 7387 JNJ Buy
## 7388 JNJ Buy
## 7389 JNJ Buy
## 7390 JNJ Buy
## 7391 JNJ Buy
## 7392 JNJ Buy
## 7393 JNJ Buy
## 7394 JNJ Buy
## 7395 JNJ Buy
## 7396 JNJ Buy
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## 7398 JNJ Buy
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## 7400 JNJ Buy
## 7401 JNJ Buy
## 7402 JNJ Buy
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## 7404 JNJ Buy
## 7405 JNJ Buy
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## 7409 JNJ Buy
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## 7424 JNJ Buy
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## 7428 JNJ Buy
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## 7449 JNJ Buy
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## 7454 JNJ Buy
## 7455 JNJ Buy
## 7456 JNJ Buy
## 7457 JNJ Buy
## 7458 JNJ Buy
## 7459 JNJ Buy
## 7460 JNJ Buy
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## 8367 JNJ Buy
## 8368 JNJ Buy
## 8369 JNJ Buy
## 8370 JNJ Buy
## 8371 JNJ Buy
## 8372 JNJ Buy
## 8373 JNJ Buy
## 8374 JNJ Buy
## 8375 JNJ Buy
## 8376 JNJ Buy
## 8377 JNJ Buy
## 8378 JNJ Buy
## 8379 JNJ Buy
## 8380 JNJ Buy
## 8381 JNJ Buy
## 8382 JNJ Buy
## 8383 JNJ Buy
## 8384 JNJ Buy
## 8385 JNJ Buy
## 8386 JNJ Buy
## 8387 JNJ Buy
## 8388 JNJ Buy
## 8389 JNJ Buy
## 8390 JNJ Buy
## 8391 JNJ Buy
## 8392 JNJ Buy
## 8393 JNJ Buy
## 8394 JNJ Buy
## 8395 JNJ Buy
## 8396 JNJ Buy
## 8397 JNJ Buy
## 8398 JNJ Buy
## 8399 JNJ Buy
## 8400 JNJ Buy
## 8401 JNJ Buy
## 8402 JNJ Buy
## 8403 JNJ Buy
## 8404 JNJ Buy
## 8405 JNJ Buy
## 8406 JNJ Buy
## 8407 JNJ Buy
## 8408 JNJ Buy
## 8409 JNJ Buy
## 8410 JNJ Buy
## 8411 JNJ Buy
## 8412 JNJ Buy
## 8413 JNJ Buy
## 8414 JNJ Buy
## 8415 JNJ Buy
## 8416 JNJ Buy
## 8417 JNJ Buy
## 8418 JNJ Buy
## 8419 JNJ Buy
## 8420 JNJ Buy
## 8421 JNJ Buy
## 8422 JNJ Buy
## 8423 JNJ Buy
## 8424 JNJ Buy
## 8425 JNJ Buy
## 8426 JNJ Buy
## 8427 JNJ Buy
## 8428 JNJ Buy
## 8429 JNJ Buy
## 8430 JNJ Buy
## 8431 JNJ Buy
## 8432 JNJ Buy
## 8433 JNJ Buy
## 8434 JNJ Buy
## 8435 JNJ Buy
## 8436 JNJ Buy
## 8437 JNJ Buy
## 8438 JNJ Buy
## 8439 JNJ Buy
## 8440 JNJ Buy
## 8441 JNJ Buy
## 8442 JNJ Buy
## 8443 JNJ Buy
## 8444 JNJ Buy
## 8445 JNJ Buy
## 8446 JNJ Buy
## 8447 JNJ Buy
## 8448 JNJ Buy
## 8449 JNJ Buy
## 8450 JNJ Buy
## 8451 JNJ Buy
## 8452 JNJ Buy
## 8453 JNJ Buy
## 8454 JNJ Buy
## 8455 JNJ Buy
## 8456 JNJ Buy
## 8457 JNJ Buy
## 8458 JNJ Buy
## 8459 JNJ Buy
## 8460 JNJ Buy
## 8461 JNJ Buy
## 8462 JNJ Buy
## 8463 JNJ Buy
## 8464 JNJ Buy
## 8465 JNJ Buy
## 8466 JNJ Buy
## 8467 JNJ Buy
## 8468 JNJ Buy
## 8469 JNJ Buy
## 8470 JNJ Buy
## 8471 JNJ Buy
## 8472 JNJ Buy
## 8473 JNJ Buy
## 8474 JNJ Buy
## 8475 JNJ Buy
## 8476 JNJ Buy
## 8477 JNJ Buy
## 8478 JNJ Buy
## 8479 JNJ Buy
## 8480 JNJ Buy
## 8481 JNJ Buy
## 8482 JNJ Buy
## 8483 JNJ Buy
## 8484 JNJ Buy
## 8485 JNJ Buy
## 8486 JNJ Buy
## 8487 JNJ Buy
## 8488 JNJ Buy
## 8489 JNJ Buy
## 8490 JNJ Buy
## 8491 JNJ Buy
## 8492 JNJ Buy
## 8493 JNJ Buy
## 8494 JNJ Buy
## 8495 JNJ Buy
## 8496 JNJ Buy
## 8497 JNJ Buy
## 8498 JNJ Buy
## 8499 JNJ Buy
## 8500 JNJ Buy
## 8501 JNJ Buy
## 8502 JNJ Buy
## 8503 JNJ Buy
## 8504 JNJ Buy
## 8505 JNJ Buy
## 8506 JNJ Buy
## 8507 JNJ Buy
## 8508 JNJ Buy
## 8509 JNJ Buy
## 8510 JNJ Buy
## 8511 JNJ Buy
## 8512 JNJ Buy
## 8513 JNJ Buy
## 8514 JNJ Buy
## 8515 JNJ Buy
## 8516 JNJ Buy
## 8517 JNJ Buy
## 8518 JNJ Buy
## 8519 JNJ Buy
## 8520 JNJ Buy
## 8521 JNJ Buy
## 8522 JNJ Buy
## 8523 JNJ Buy
## 8524 JNJ Buy
## 8525 JNJ Buy
## 8526 JNJ Buy
## 8527 JNJ Buy
## 8528 JNJ Buy
## 8529 JNJ Buy
## 8530 JNJ Buy
## 8531 JNJ Buy
## 8532 JNJ Buy
## 8533 JNJ Buy
## 8534 JNJ Buy
## 8535 JNJ Buy
## 8536 JNJ Buy
## 8537 JNJ Buy
## 8538 JNJ Buy
## 8539 JNJ Buy
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## 8543 JNJ Buy
## 8544 JNJ Buy
## 8545 JNJ Buy
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## 8547 JNJ Buy
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## 8549 JNJ Buy
## 8550 JNJ Buy
## 8551 JNJ Buy
## 8552 JNJ Buy
## 8553 JNJ Buy
## 8554 JNJ Buy
## 8555 JNJ Buy
## 8556 JNJ Buy
## 8557 JNJ Buy
## 8558 JNJ Buy
## 8559 JNJ Buy
## 8560 JNJ Buy
## 8561 JNJ Buy
## 8562 JNJ Buy
## 8563 JNJ Buy
## 8564 JNJ Buy
## 8565 JNJ Buy
## 8566 JNJ Buy
## 8567 JNJ Buy
## 8568 JNJ Buy
## 8569 JNJ Buy
## 8570 JNJ Buy
## 8571 JNJ Buy
## 8572 JNJ Buy
## 8573 JNJ Buy
## 8574 JNJ Buy
## 8575 JNJ Buy
## 8576 JNJ Buy
## 8577 JNJ Buy
## 8578 JNJ Buy
## 8579 JNJ Buy
## 8580 JNJ Buy
## 8581 JNJ Buy
## 8582 JNJ Buy
## 8583 JNJ Buy
## 8584 JNJ Buy
## 8585 JNJ Buy
## 8586 JNJ Buy
## 8587 JNJ Buy
## 8588 JNJ Buy
## 8589 JNJ Buy
## 8590 JNJ Buy
## 8591 JNJ Buy
## 8592 JNJ Buy
## 8593 JNJ Buy
## 8594 JNJ Buy
## 8595 JNJ Buy
## 8596 JNJ Buy
## 8597 JNJ Buy
## 8598 JNJ Buy
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## 8600 JNJ Buy
## 8601 JNJ Buy
## 8602 JNJ Buy
## 8603 JNJ Buy
## 8604 JNJ Buy
## 8605 JNJ Buy
## 8606 JNJ Buy
## 8607 JNJ Buy
## 8608 JNJ Buy
## 8609 JNJ Buy
## 8610 JNJ Buy
## 8611 JNJ Buy
## 8612 JNJ Buy
## 8613 JNJ Buy
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## 8615 JNJ Buy
## 8616 JNJ Buy
## 8617 JNJ Buy
## 8618 JNJ Buy
## 8619 JNJ Buy
## 8620 JNJ Buy
## 8621 JNJ Buy
## 8622 JNJ Buy
## 8623 JNJ Buy
## 8624 JNJ Buy
## 8625 JNJ Buy
## 8626 JNJ Buy
## 8627 JNJ Buy
## 8628 JNJ Buy
## 8629 JNJ Buy
## 8630 JNJ Buy
## 8631 JNJ Buy
## 8632 JNJ Buy
## 8633 JNJ Buy
## 8634 JNJ Buy
## 8635 JNJ Buy
## 8636 JNJ Buy
## 8637 JNJ Buy
## 8638 JNJ Buy
## 8639 JNJ Buy
## 8640 JNJ Buy
## 8641 JNJ Buy
## 8642 JNJ Buy
## 8643 JNJ Buy
## 8644 JNJ Buy
## 8645 JNJ Buy
## 8646 JNJ Buy
## 8647 JNJ Buy
## 8648 JNJ Buy
## 8649 JNJ Buy
## 8650 JNJ Buy
## 8651 JNJ Buy
## 8652 JNJ Buy
## 8653 JNJ Buy
## 8654 JNJ Buy
## 8655 JNJ Buy
## 8656 JNJ Buy
## 8657 JNJ Buy
## 8658 JNJ Buy
## 8659 JNJ Buy
## 8660 JNJ Buy
## 8661 JNJ Buy
## 8662 JNJ Buy
## 8663 JNJ Buy
## 8664 JNJ Buy
## 8665 JNJ Buy
## 8666 JNJ Buy
## 8667 JNJ Buy
## 8668 JNJ Buy
## 8669 JNJ Buy
## 8670 JNJ Buy
## 8671 JNJ Buy
## 8672 JNJ Buy
## 8673 JNJ Buy
## 8674 JNJ Buy
## 8675 JNJ Buy
## 8676 JNJ Buy
## 8677 JNJ Buy
## 8678 JNJ Buy
## 8679 JNJ Buy
## 8680 JNJ Buy
## 8681 JNJ Buy
## 8682 JNJ Buy
## 8683 JNJ Buy
## 8684 JNJ Buy
## 8685 JNJ Buy
## 8686 JNJ Buy
## 8687 JNJ Buy
## 8688 JNJ Buy
## 8689 JNJ Buy
## 8690 JNJ Buy
## 8691 JNJ Buy
## 8692 JNJ Buy
## 8693 JNJ Buy
## 8694 JNJ Buy
## 8695 JNJ Buy
## 8696 JNJ Buy
## 8697 JNJ Buy
## 8698 JNJ Buy
## 8699 JNJ Buy
## 8700 JNJ Buy
## 8701 JNJ Buy
## 8702 JNJ Buy
## 8703 JNJ Buy
## 8704 JNJ Buy
## 8705 JNJ Buy
## 8706 JNJ Buy
## 8707 JNJ Buy
## 8708 JNJ Buy
## 8709 JNJ Buy
## 8710 JNJ Buy
## 8711 JNJ Buy
## 8712 JNJ Buy
## 8713 JNJ Buy
## 8714 JNJ Buy
## 8715 JNJ Buy
## 8716 JNJ Buy
## 8717 JNJ Buy
## 8718 JNJ Buy
## 8719 JNJ Buy
## 8720 JNJ Buy
## 8721 JNJ Buy
## 8722 JNJ Buy
## 8723 JNJ Buy
## 8724 JNJ Buy
## 8725 JNJ Buy
## 8726 JNJ Buy
## 8727 JNJ Buy
## 8728 JNJ Buy
## 8729 JNJ Buy
## 8730 JNJ Buy
## 8731 JNJ Buy
## 8732 JNJ Buy
## 8733 JNJ Buy
## 8734 JNJ Buy
## 8735 JNJ Buy
## 8736 JNJ Buy
## 8737 JNJ Buy
## 8738 JNJ Buy
## 8739 JNJ Buy
## 8740 JNJ Buy
## 8741 JNJ Buy
## 8742 JNJ Buy
## 8743 JNJ Buy
## 8744 JNJ Buy
## 8745 JNJ Buy
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## 8747 JNJ Buy
## 8748 JNJ Buy
## 8749 JNJ Buy
## 8750 JNJ Buy
## 8751 JNJ Buy
## 8752 JNJ Buy
## 8753 JNJ Buy
## 8754 JNJ Buy
## 8755 JNJ Buy
## 8756 JNJ Buy
## 8757 JNJ Buy
## 8758 JNJ Buy
## 8759 JNJ Buy
## 8760 JNJ Buy
## 8761 JNJ Buy
## 8762 JNJ Buy
## 8763 JNJ Buy
## 8764 JNJ Buy
## 8765 JNJ Buy
## 8766 JNJ Buy
## 8767 JNJ Buy
## 8768 JNJ Buy
## 8769 JNJ Buy
## 8770 JNJ Buy
## 8771 JNJ Buy
## 8772 JNJ Buy
## 8773 JNJ Buy
## 8774 JNJ Buy
## 8775 JNJ Buy
## 8776 JNJ Buy
## 8777 JNJ Buy
## 8778 JNJ Buy
## 8779 JNJ Buy
## 8780 JNJ Buy
## 8781 JNJ Buy
## 8782 JNJ Buy
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## 8785 JNJ Buy
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## 8787 JNJ Buy
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## 8789 JNJ Buy
## 8790 JNJ Buy
## 8791 JNJ Buy
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## 8794 JNJ Buy
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## 8796 JNJ Buy
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## 8802 JNJ Buy
## 8803 JNJ Buy
## 8804 JNJ Buy
## 8805 JNJ Buy
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## 8807 JNJ Buy
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## 8809 JNJ Buy
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## 8821 JNJ Buy
## 8822 JNJ Buy
## 8823 JNJ Buy
## 8824 JNJ Buy
## 8825 JNJ Buy
## 8826 JNJ Buy
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## 8828 JNJ Buy
## 8829 JNJ Buy
## 8830 JNJ Buy
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## 8835 JNJ Buy
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## 8852 JNJ Buy
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## 8861 JNJ Buy
## 8862 JNJ Buy
## 8863 JNJ Buy
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## 8870 JNJ Buy
## 8871 JNJ Buy
## 8872 JNJ Buy
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## 8876 JNJ Buy
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## 8879 JNJ Buy
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## 8907 JNJ Buy
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## 8957 JNJ Buy
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## 8965 JNJ Buy
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## 8967 JNJ Buy
## 8968 JNJ Buy
## 8969 JNJ Buy
## 8970 JNJ Buy
## 8971 JNJ Buy
## 8972 JNJ Buy
## 8973 JNJ Buy
## 8974 JNJ Buy
## 8975 JNJ Buy
## 8976 JNJ Buy
## 8977 JNJ Buy
## 8978 JNJ Buy
## 8979 JNJ Buy
## 8980 JNJ Buy
## 8981 JNJ Buy
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## 8983 JNJ Buy
## 8984 JNJ Buy
## 8985 JNJ Buy
## 8986 JNJ Buy
## 8987 JNJ Buy
## 8988 JNJ Buy
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## 8990 JNJ Buy
## 8991 JNJ Buy
## 8992 JNJ Buy
## 8993 JNJ Buy
## 8994 JNJ Buy
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## 8997 JNJ Buy
## 8998 JNJ Buy
## 8999 JNJ Buy
## 9000 JNJ Buy
## 9001 JNJ Buy
## 9002 JNJ Buy
## 9003 JNJ Buy
## 9004 JNJ Buy
## 9005 JNJ Buy
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## 9012 JNJ Buy
## 9013 JNJ Buy
## 9014 JNJ Buy
## 9015 JNJ Buy
## 9016 JNJ Buy
## 9017 JNJ Buy
## 9018 JNJ Buy
## 9019 JNJ Buy
## 9020 JNJ Buy
## 9021 JNJ Buy
## 9022 JNJ Buy
## 9023 JNJ Buy
## 9024 JNJ Buy
## 9025 JNJ Buy
## 9026 JNJ Buy
## 9027 JNJ Buy
## 9028 JNJ Buy
## 9029 JNJ Buy
## 9030 JNJ Buy
## 9031 JNJ Buy
## 9032 JNJ Buy
## 9033 JNJ Buy
## 9034 JNJ Buy
## 9035 JNJ Buy
## 9036 JNJ Buy
## 9037 JNJ Buy
## 9038 JNJ Buy
## 9039 JNJ Buy
## 9040 JNJ Buy
## 9041 JNJ Buy
## 9042 JNJ Buy
## 9043 JNJ Buy
## 9044 JNJ Buy
## 9045 JNJ Buy
## 9046 JNJ Buy
## 9047 JNJ Buy
## 9048 JNJ Buy
## 9049 JNJ Buy
## 9050 JNJ Buy
## 9051 JNJ Buy
## 9052 JNJ Buy
## 9053 JNJ Buy
## 9054 JNJ Buy
## 9055 JNJ Buy
## 9056 JNJ Buy
## 9057 JNJ Buy
## 9058 JNJ Buy
## 9059 JNJ Buy
## 9060 JNJ Buy
## 9061 JNJ Buy
## 9062 JNJ Buy
## 9063 JNJ Buy
## 9064 JNJ Buy
## 9065 JNJ Buy
## 9066 JNJ Buy
## 9067 JNJ Buy
## 9068 JNJ Buy
## 9069 JNJ Buy
## 9070 JNJ Buy
## 9071 JNJ Buy
## 9072 JNJ Buy
## 9073 JNJ Buy
## 9074 JNJ Buy
## 9075 JNJ Buy
## 9076 JNJ Buy
## 9077 JNJ Buy
## 9078 JNJ Buy
## 9079 JNJ Buy
## 9080 JNJ Buy
## 9081 JNJ Buy
## 9082 JNJ Buy
## 9083 JNJ Buy
## 9084 JNJ Buy
## 9085 JNJ Buy
## 9086 JNJ Buy
## 9087 JNJ Buy
## 9088 JNJ Buy
## 9089 JNJ Buy
## 9090 JNJ Buy
## 9091 JNJ Buy
## 9092 JNJ Buy
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## 9094 JNJ Buy
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## 9096 JNJ Buy
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## 9100 JNJ Buy
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## 9102 JNJ Buy
## 9103 JNJ Buy
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## 9111 JNJ Buy
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## 9151 JNJ Buy
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## 9209 JNJ Buy
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## 9222 JNJ Buy
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## 9265 JNJ Buy
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## 9275 JNJ Buy
## 9276 JNJ Buy
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5.2 Summary tables for action taken
The table shows the frequency of each action (“Buy”, “Sell”, “Hold”) taken for each stock. For instance, for the stock “AAPL”, the algorithm took the action “Buy” 2958 times, “Sell” 157 times, and “Hold” 156 times during the simulation. The same information is presented for the other three stocks (“AMZN”, “JNJ”, and “NFLX”).
| AAPL | AMZN | JNJ | NFLX | |
|---|---|---|---|---|
| Buy | 2958 | 2958 | 2958 | 2958 |
| Sell | 157 | 157 | 157 | 157 |
| Hold | 156 | 156 | 156 | 156 |
5.3 Plot for predicted closing prices and Adjusted prices
The plots shows that the algorithm was able to predict closing prices with significant accuracy since the predicted closing prices are not deviating too much from the adjusted prices.
5.4 Performance Check
We show the performance of the predictions using mean squared error for four stocks (AAPL, AMZN, JNJ, and NFLX). For each stock, the code first predicts the prices using the Q matrices trained on the training data (2010 to 2016) and then calculates the mean squared error between the predicted prices and the actual prices in the testing data (2017 to 2022).
The mean squared error for AAPL is 161.2266, for AMZN it is 1006.65, for JNJ it is 3317.487, and for NFLX it is 91061.72. A lower mean squared error indicates better performance, therefore the predictions for AAPL are the most accurate among the four stocks.
5.5 Implementation of SARSA
The SARSA code provided is an implementation of the SARSA (State-Action-Reward-State-Action) reinforcement learning algorithm to train an agent to make buy, sell, or hold decisions for the stocks used in this project. The code is set up to train the agent on a subset of the data (2010-2016) and test the agent on the remaining data (2017-2022).
# extract closing prices from data
closing_prices <- train$close
# define state based on previous 3 closing prices
define_state <- function(closing_prices, i) {
if (i < 4) {
# if not enough data points yet, use the first one as the state
state <- closing_prices[1]
} else {
# use previous 3 closing prices as the state
state <- closing_prices[(i-3):i]
}
return(state)
}Next, we defined the tune function that takes in a
dataset, a range of values for the learning rate (alpha), discount
factor (gamma), and epsilon-greedy policy (epsilon). The function uses
nested loops to iterate over each combination of alpha, gamma, and
epsilon values and runs the SARSA algorithm on the dataset using those
hyperparameters. The function then calculates the total reward obtained
by the SARSA algorithm and stores the hyperparameters and
the total reward as a list in the “results” variable.
After performing the hyperparameter tuning, the optimal combination
of hyperparameters that yielded the highest total reward for the
SARSA algorithm were; \(\alpha=
0.8\), \(\gamma= 0.3\), and
\(\epsilon =0.1\). These were
associated with the highest total reward of 21069.54.
# function that extracts the hyperparameters associated with the best result and returns them as a list
tune <- function(data, alpha_range, gamma_range, epsilon_range) {
# initialize results list
results <- list()
# loop through alpha, gamma, and epsilon values
for (alpha in alpha_range) {
for (gamma in gamma_range) {
for (epsilon in epsilon_range) {
# run SARSA algorithm with current hyperparameters
trades_and_Q <- sarsa(data, alpha = alpha, gamma = gamma, epsilon = epsilon)
# calculate total reward and store results
total_reward <- sum(unlist(lapply(trades_and_Q$trades, function(x) x$reward)))
results[[length(results)+1]] <- list(alpha = alpha, gamma = gamma, epsilon = epsilon, total_reward = total_reward)
}
}
}
# return hyperparameters with highest total reward
best_result_idx <- which.max(sapply(results, function(x) x$total_reward))
best_result <- results[[best_result_idx]]
return(list(alpha = best_result$alpha, gamma = best_result$gamma, epsilon = best_result$epsilon, total_reward = best_result$total_reward))
}We then used the combination of the best hyperparameters to train the
algorithm on the train test. The figure below shows the algorithm made a
higher number of buy trading actions compared to the
sell actions.
To test the SARSA algorithm on the test data, we
modified the sarsa function to use the learned Q-table to
choose actions based on the current state instead of using the
epsilon-greedy policy. Here, we removed the Q-table
initialization and epsilon-greedy policy from the original
sarsa function, and added an additional input parameter Q
to the sarsa_test function to take in the learned Q-table.
To test the SARSA algorithm on the test data, we can call
the sarsa_test function with the test data and the learned
Q-table as input:
The portfolio value over time represents the value of the portfolio as it changes over the period of the test data. It shows how the agent’s decisions based on the SARSA algorithm impacted the portfolio’s value. A higher portfolio value means that the agent’s decisions led to more profitable trades and a better overall outcome.
From the above results; while the code may be able to generate some predictions on the test data, it is important to keep in mind that SARSA is a model-free algorithm, meaning that it does not explicitly model the underlying dynamics of the stock market. Instead, it learns through trial and error by exploring different actions and observing the resulting rewards.
Limitation: It is difficult to make definitive predictions on the test data using this code alone. It would be more appropriate to evaluate the performance of the agent on the test data by analyzing its trades and portfolio value over time and comparing it to a benchmark such as a buy-and-hold strategy. Additionally, it would be useful to further analyze the agent’s behavior and performance by adjusting the hyperparameters (alpha, gamma, and epsilon) and potentially using alternative reinforcement learning algorithms or additional features.
5.6 Implementation of DQN
Next, we used tensorflow package in python to implement
the DQN on our stock data. However, since training on the full train
data set was not feasible due to computational time and memory capacity,
we trained the DQN on one stock, NFLX. To reproduce the same using other
stocks, all one has to do is just select the stock they want from the
drop down widget created in the DQN file. We used the
same train/test splits as in the previous sections.
The code in the DQN file defines a class
Agent which implements a Q-learning algorithm for trading
in financial markets.The __init__ method initializes the
hyperparameters and the neural network architecture. act
method selects an action based on the current state and
get_state method returns the current state.
replay method trains the Q-network. buy method
buys or sells shares according to the action selected by the
Q-network.
The main logic of the code is in the buy method, which
takes the initial money and tries to buy and sell shares at different
time steps based on the Q-network’s decisions. The actions can be to
buy, sell, or do nothing. The
shares are bought if the Q-network selects action 1 and if the price is
less than the available initial money. The shares are sold if the
Q-network selects action 2 and if there are shares in the inventory. The
profit or loss is calculated based on the price at which the shares are
bought and sold. The overall rewards are stored in the total profit
variable.
The code also includes a neural network architecture with several
hidden layers and uses the TensorFlow library for deep
learning. We tested the performance of 4 different architectures, with
Adam chosen as our chosen gradient descent algorithm as shown in the
snip below. Results of our evaluation are presented below for our four
network architectures:
Below are the performance results for the different architectures;
We found the best architecture to be the fourth one; the one with two neural networks, with 512 neurons in the first layer and 256 in the second layer. The metrics used to compare our models were the total gains in terms of total investment which were observed over the trading days across each 50 Episode period during training. The fourth architecture had 60.97% gains in investment during training.
Next, we tested the best network architecture on the test data.
# test the agent
states_buy_test, states_sell_test, total_gains_test, invest_test = test_agent.buy(initial_money = initial_money)Below is a snip of how the agent was trading in the test data for the first 35 days.
For the Netflix stocks, the figure below shows the trading decisions made by the agent in the test data.
We observe that in the test data, the agent achieved a 14.96% gains in total investments.
6 References
7 Session Info
## R version 4.2.0 (2022-04-22 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 19045)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.utf8
## [2] LC_CTYPE=English_United States.utf8
## [3] LC_MONETARY=English_United States.utf8
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.utf8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] tidyquant_1.0.7 PerformanceAnalytics_2.0.4
## [3] lubridate_1.9.2 cowplot_1.1.1
## [5] knitr_1.42 reshape2_1.4.4
## [7] gridExtra_2.3 fBasics_4022.94
## [9] htmltools_0.5.4 DT_0.27
## [11] dplyr_1.1.0 ggplot2_3.4.1
## [13] ReinforcementLearning_1.0.5 quantmod_0.4.20
## [15] TTR_0.24.3 xts_0.13.0
## [17] zoo_1.8-11
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.10 lattice_0.20-45 digest_0.6.31
## [4] utf8_1.2.3 R6_2.5.1 plyr_1.8.8
## [7] evaluate_0.20 httr_1.4.5 pillar_1.8.1
## [10] rlang_1.1.0 spatial_7.3-15 curl_5.0.0
## [13] rstudioapi_0.14 jquerylib_0.1.4 hash_2.2.6.2
## [16] rmarkdown_2.20 stringr_1.5.0 htmlwidgets_1.6.1
## [19] munsell_0.5.0 compiler_4.2.0 xfun_0.37
## [22] pkgconfig_2.0.3 tidyselect_1.2.0 tibble_3.2.0
## [25] bookdown_0.33 quadprog_1.5-8 fansi_1.0.4
## [28] withr_2.5.0 grid_4.2.0 Quandl_2.11.0
## [31] jsonlite_1.8.4 gtable_0.3.1 lifecycle_1.0.3
## [34] magrittr_2.0.3 scales_1.2.1 rmdformats_1.0.4
## [37] cli_3.6.0 stringi_1.7.12 cachem_1.0.7
## [40] timeDate_4022.108 bslib_0.4.2 generics_0.1.3
## [43] vctrs_0.6.0 tools_4.2.0 glue_1.6.2
## [46] fastmap_1.1.1 yaml_2.3.7 timechange_0.2.0
## [49] colorspace_2.1-0 timeSeries_4021.105 sass_0.4.5